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EDUCATION.
1966-70 National Taiwan University, B.S.,
1970-71 National Taiwan University, Graduate School in Mathematics;
1971-74 University of California, Berkeley, Ph.D.
These Advisor: Andrew P. Ogg
RESEARCH INTERESTS.
Automorphic Forms, Number Theory, Representation Theory, Coding Theory and Graph Theory
EMPLOYMENT.
1974-77 Assistant Professor, Benjamin Pierce Lecturer, Harvard University;
1978 Member, Institute for Advanced Study, Princeton, N. J.;
1978-79 Assistant Professor, University of Illinois at Chicago;
1979-84 Associate Professor, Pennsylvania State University;
1984- Professor, Pennsylvania State University
CONCURRENT.
Visiting Inst. of Math., Bonn, Germany, summer of 1977 and 1983;
Visiting Harvard University, fall, 1981;
Visiting Inst. des Hautes Etudes Scientifiques, France, fall 1982;
Visiting Inst. for Advanced Study, Princeton, spring 1984, spring 2000 (sabbatical leave);
Visiting National Tsinhua University, Taiwan, summer 1984;
Visiting Univ. de Paris-Sud, Centre d’Orsay, France, 1985-86 (sabbatical leave);
Visiting Stanford University, summer 1986;
Visiting Academia Sinica, Taiwan, summer of 1988, 1990, 1994, 1997;
Visiting Nankai Inst. of Math., Tianjin, China, spring 1990, 1993;
Visiting Academia Sinica, Beijing, China, 1990, 1992, 1997;
Visiting University of Pennsylvania, 1991-92 (under NSF VPW award);
Visiting Sichuan University, China, summer 1992;
Visiting National Taiwan University, 1992-93 (sabbatical leave);
Consultant at AT&T Bell Laboratories and AT&T Shannon Laboratories, N. J.
Visiting Mathematical Sciences Research Institute, Berkeley, CA, spring 1995;
Visiting the National Center of Theoretical Sciences, Mathematics Division, Taiwan,
Summer and Dec. 1998, Aug 1999-Jan 2000 (sabbatical leave), Aug 2001, Aug 2002, Aug. 2003, July 2005;
Visiting Tamkang University, Taipei, Taiwan, summer, 2000;
Visiting the National Center of Theoretical Sciences at Taipei, National Taiwan University, July 2004
HONORS.
Alrfed Sloan Fellow, 1981-83;
Invited Half-hour Speaker at the XI International Symposium on Mathematical
Programming, August, 1982, Bonn, West Germany;
NSF Visiting Professorship for Women Award, 1991-92;
Editor of Transactions of Amer. Math. Soc., 1992-96;
Editor of Taiwanese Journal of Mathematics, 1998-;
Editor of Proceedings of Amer. Math. Soc., 2002-;
Editor of International Journal of Number Theory, 2005-;
Distinguished Visiting Professor at National Tsinghua University, Taiwan, Aug 1999-Jan 2000;
PUBLICATIONS.
 [1] |
Newforms and functional equations, Math. Ann. 212, 285-315 (1975) |
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[2]
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On modular functions in characteristic p, Trans. Amer. Math. Soc. 246, 231-259 (1978) |
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[3]
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(with A.O.L. Atkin) Twists of newforms and pseudo-eigenvalues of W-operators, Invent, Math. 48, 221-243 (1978) |
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[4]
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Eisenstein series and decomposition theory over function fields, Math. Ann. 240, 115-139 (1979) |
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[5]
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L-series of Rankin type and their functional equations, Math. Ann. 244, 135-166 (1979) |
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[6]
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On the representations of GL(2), Part I: "-factors and n-closeness, J. reine ang. Math. 313, 27-42 (1980) |
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[7]
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On the representations of GL(2), Part II: "-factors of the representations of GL(2) × GL(2), J. reine ang. Math. 314, 3-20(1980) |
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[8] |
(with R.L. Graham and S.-Y. R. Li) On the structure of t-designes, SIAM J. Alg. and Disc. Meth. 1(1), 8-14 (1980) |
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[9] |
Hecke-Weil-Jacquet-Langlands theorem revisited. In: Lectures Notes in Math. 751, 206-220, Springer-Verlag, N. Y. (1979) |
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[10] |
Une caracterisation des representations automorphes de GL1 et GL2, C.R. Acad. Sci. Serie A 29, 681-684 (1980) |
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[11]
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(with G. Harder and J. Weisinger) Dimensions of spaces of cusp forms over function fields, J. reine ang. Math. 319, 73-103 (1980) |
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[12]
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(with S.-Y. R. Li) On generators of ideals associated with unions of linear varieties, Bull. London Math. Soc. 13, 59-65 (1981) |
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[13] |
On a theorem of Hecke-Weil-Jacquet-Langlands. In: Recent Progress in Analytic Number Theory, vol. 2, 119-152, Academic Press (1980) |
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[14]
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(with S.-Y. R. Li) Independence numbers of graphs and generators of ideals, Combinatorica 1, 55-61 (1981) |
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[15] |
(with E. Formanek and P. Halpin) The Poincare series of the ring of 2 × 2 generic matrices, J. Alg. 69, 105-112 (1981) |
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[16]
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On converse theorems for GL(2) and GL(1), Amer. J. Math. 103, no. 5, 851-885 (1981) |
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[17]
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(with R. L. Graham and J. L. Paul) Homogeneous collinear sets in partitions of Zn, J. Combinatorial Theory, Series A, vol. 31, 21-32 (1981) |
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[18]
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Generators for the ideal of polynomial identities satisfied by 2 × 2 matrices, J. Alg. 74, no. 1, 2446-263 (1982) |
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[19]
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(with R.L. Graham and J.L. Paul) Monochromatic lines in partitions of Zn. In: Lecture Notes in Math. 884, 35-48, Springer-Verlag, N. Y. (1981) |
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[20]
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(with J. Soto-Andrade) Barnes identities and representations of GL2. Part I: Finite field case, J. reine ang. Math. 344, 171-179 (1983) |
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[21]
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Barnes identities and representations of GL2. Part II: Nonarchimedean local field case, J. reine ang. Math. 345, 69-92 (1983) |
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[22]
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Determination of the residue classes of a polynomial at integral arguments, Disc. Math. 47, 83-90 (1983) |
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[23]
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Diagonalizing modular forms, J. Alg. 99, no. 1, 210-231 (1986) |
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[24]
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(with B. Z. Moroz) On ideal classes of number fields containing integral ideals of equal norms, J. Number Theory 21, 185-203 (1985) |
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[25]
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A criterion for automorphic representations of GL(1) and GL(2), S’em. de Th’eorie des Nombres de Bordeaux, 1982-83, expos’e no. 7 (1984) |
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[26]
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(with P. G’erardin) Fourier transforms of representations of quaternions, J. reine ang. Math. 359, 121-173 (1985) |
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[27]
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A criterion on automorphic forms for GL1 and GL2 over global fields. In: S’em. de Th’eorie des Nombres de Paris 1982-83, Progress in Math., vol. 51, 161-172, Birkhauser, Boston (1984) |
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[28]
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(with P. G’erardin) A functional equation for degree two local factors, Canad. Math. Soc. Bull., vol. 28(3), 355-371 (1985) |
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[29]
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(with P. G’erardin) Establishing correspondences without the trace formula, AMS Contemporary Math. 53, 185-200 (1986) |
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[30]
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Various aspects of Barnes’ identity. In: S’em. de Th’eorie des Nombres de Paris 1984-85, Progress in Math., vol. 63, 187-203, Birkhauser, Boston (1986) |
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[31] |
(with P. G’erardin) Identities on degree two local factors. In: Proceedings of the conference on ”Representation Theory and Number Theory in connection with Local Langlands Conjecture”, held at Irsee, West Germany, Dec. 15-20, 1985, in AMS Contemporary Math. 86 (1989), 225-248 |
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[32]
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(with P. G’erardin) Identities on quadratic Gauss sums, Transactions Amer. Math. Soc., vol. 321, no. 1, 159-182 (1990) |
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[33] |
(with P. G’erardin) Degree two monomial representations of local Weil groups, J. f‥ur reine und angewandt Math. 394 (1989), 1-30 |
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[34]
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On quadratic Gauss sums over local fields. In : S’em. de Th’eorie des Nombres de Paris 1985-86, Progress in Math., vol. 71, 133-145, Birkhauser, Boston (1987) |
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[35]
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(with P. G’erardin) Functional equations and periodic sequences, in: Th’eorie des nombres . Number Theory (Proceedings of the International Congress on Number Theory, held in Quebec City, Canada, July 5-18, 1987), J.-M. De Koninck & C. Levesque ed., 267-279, Walter de Gruyter, Berlin, New York (1989) |
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[36]
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(with P. G’erardin) Twisted Dirichlet series and distributions, CompositioMathematica 73, 271-293 (1990) |
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[37]
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The role of Fourier transform in correspondences of representations of degree two algebras, in: Algebra, Analysis and Geometry, M.-C. Kang and K.-W. Lih edited, 121-136, World Scientific, Singapore, New Jersey, London, Hong Kong, 1989 |
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[38]
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On local exceptional representations of GL(2), preprint |
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[39]
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On local modular representations of GL(2), preprint |
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[40]
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(with A. Harnchoowong) Sylow subgroups of ideal class groups with moduli, J. Number Theory, vol. 36, no. 3, 354-372 (1990) |
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[41]
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Character sums and abelian Ramanujan graphs, J. Number Theory 41 (1992), 199-214 |
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[42]
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(with K. Feng) Eigenvalues of regular directed graphs, Appendix to no. 41, J. Number Theory 41 (1992), 214-217 |
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[43]
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(with F. K. Hwang) Hamiltonian circuits for 2-regular interconnection networks, in: Network Optimization Problems, Algorithms, Applications and Complexity, D.-Z. Du and P. M. Pardalos edited, World Scientific, Singapore, New Jersey, London, Hong Kong, 1993 |
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[44]
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(with F. K. Hwang) Reliabilities of double loop networks, Prob. Eng. and Info. Sci. 5 (1991), 255-272. |
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[45]
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Ideal class groups and Galois modules. In: S’eminaire de Th’eorie des Nombres Paris 1989-90, Progress in Math., 163-176, Birkhauser, Boston, Basel, Berlin, 1992. |
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[46]
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(with X.-D. Hu and F. K. Hwang) Most reliable double loop networks in survival reliability, Network, vol. 23 (1993), 451-458. |
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[47]
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(with F. K. Hwang) 2-connectivities of extended double loop networks. In: Combinatorial Network Theory, D.-Z. Du and F. D. Hsu eds, 107-124, Kluwer Academic Publishers, 1995. |
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[48]
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(with A. R. Calderbank, P. Frankl, R. L. Graham, and L. A. Shepp) The Sperner capacity of linear and nonlinear codes for the cyclic triangle, J. of Algebraic Combinatorics 2 (1993), 31-48. |
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[49]
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(with R. W. Chen and F. K. Hwang) Consecutive-2-out-of-n: F systems with node and link failures, IEEE Trans. Rel. vol. 42, No. 3 (1993), 497-502. |
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[50]
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(with R. W. Chen and F. K. Hwang) A reversible model for consecutive-2-out-of-n: F systems with node and link failures, Prob. Eng. and Info. Sci., 8 (1994), 189-200. |
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[51]
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(with F. K. Hwang) Connectivity reliabilities and Hamiltonian reliabilities of linear and circular consecutive-2 link systems, International Journal of Reliability, Quality and Safety Engineering, vol 1, no. 2(1994), 247-256. |
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[52]
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Number-theoretic constructions of Ramanujan graphs. In: Columbia University Number Theory Seminar, New York 1992, Ast’erisque, vol. 228 (1995), Soc. Math. de France, 101-120. |
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[53]
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(with Keqin Feng) Spectra of hypergraphs and applications, J. Number Theory, vol. 60 (1996), 1-22. |
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[54]
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Number Theory with Applications (book), World Scientific, Singapore-New Jersey -London-Hong Kong, 1996. |
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[55]
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A survey of Ramanujan graphs. In: Arithmetic, Geometry and Coding Theory, Proceedings of International Conference held at Luminy, France, June 28 - July 2, 1993, de Gruyter, Berlin-New York, 127-143, 1996 |
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[56]
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(with P. Sol’e) Spectra of regular graphs and hypergraphs and orthogonal polynomials, European Journal of Combinatorics, vol. 17 (1996). 461-477. |
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[57]
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European Journal of Combinatorics, vol. 17 (1996). 461-477. 57. (with S. Burr, P. Erd‥os and R. L. Graham) Complete sequences of sets of integer powers, Acta Arithmetica 77, vol. 2 (1996), 133-138. |
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[58]
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(with M-K Leu) On the series for L(1,), Nagoya Math. J., vol. 141 (1996), 125-142. |
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[59]
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(with R. Calderbank and B. Poonen) A 2-adic approach to the analysis of cyclic codes, IEEE Information Theory, vol. 43, no. 3 (1997), 977-986. |
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[60]
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Estimates of character sums arising from finite upper half planes. In: Finite Fields and Applications, Proc. of the third international conference, Glasgow, 11-14 July, 1995, S. Cohen and H. Niederreiter eds., Lecture Note Series 233, London Math. Soc., Cambridge Univ. Press, 219-228, 1996. |
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[61]
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Character sums over p-adic fields, Journal of Number Theory, vol. 74, 181-229 (1999). |
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[62]
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Geometry, graph theory and number theory. In: Algebra and Geometry (Taipei 1995), 83-102, Lect. Alg. Geom. 2, Internat. Press, Cambridge, MA. 1998. |
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[63]
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(with B. Gao, F. Hwang and U. Rothblum) Partition-polytopes over 1-dimensional points, Mathematical Programming 85 (1999), no. 2, Ser. A, 335-362. |
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[64]
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In Search of randomness: distributions of eigenvalues. In: Proc. of International Conference on Aspects of Mathematics, June 10-13, 1996, Hong Kong University, Hong Kong, 197-222 (2002). |
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[65]
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Elliptic curves, Kloosterman sums and Ramanujan graphs. In: Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A. O. L. Atkin, D. A. Buell and J. T. Teitelbaum edited, AMS/IP Studies in Advanced Math., vol. 7, Amer. Math. Soc., Providence (1998), 179-190. |
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[66]
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Eigenvalues of Ramanujan graphs. In: Emerging Applications of Number Theory (Minneapolis, MN, 1996), 387-403, IMA Vol. Math. Appl. 109, Springer, New York, 1999. |
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[67]
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(with Ching-Li Chai) Function fields: arithmetic and applications, Contemporary Math. 245, 189-199 (1999) |
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[68]
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Exponential sum estimates and applications, Proc. of 35th Annual Allerton Conference on Communication, Control and Computing, Sept. 29-Oct 1, 1997, Universityof Illinois at Urbana-Champaign, 14-22, 1998. |
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[69]
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(with Xuning Feng) On Z4 codes with large Lee weight, preprint. |
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[70]
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(with Hiren Maharaj) Coverings of curves with asymptotically many rational points, Journal of Number Theory 96, 232-256 (2002). |
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[71]
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Various constructions of good codes. Contemporary Math., vol. 264, 271-285, (2000). |
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[72]
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Recent developments in automorphic forms and applications, Number Theory for the Millennium II, M. A. Bennett et al. eds., A K Peters, Boston, 2002, 331-354. |
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[73]
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Recent developments in automorphic forms and applications, Surveys in Number Theory: Papers from The Millennial Conference on Number Theory, Bennett et al. editors, A K Peters, Boston, 2002, 125-148. |
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[74]
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(with C.-L. Chai) Character sums, automorphic forms, equidistribution, and Ramanujan graphs, Part I. The Kloosterman sum conjecture over function fields, Forum Math 15, Issue 5 (2003), 679-699. |
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[75]
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(with C.-L. Chai) Character sums, automorphic forms, equidistribution, and Ramanujan graphs, Part II. Eigenvalues of Terras graphs, Forum Math. 16 (2004), 631-661. |
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[76]
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The arithmetic of modular forms, IAS/Park City Mathematics Series Volume 9, Arithmetic Algebraic Geometry, 479-504, 2001. |
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[77]
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On negative eigenvalues of regular graphs, C. R. Acad. Sci. Paris, t. 333, S’erie I, 907-912, 2001. |
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[78]
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(with H. Maharaj and H. Stichtenoth, and an appendix by N. Elkies) New optimal tame towers of function fields over small finite fields, Lecture Notes in Computer 4 Science 2369 (Proceedings of the 5th conference on Algorithmic Number Theory Symposium, 2002) C.Fieker and D.R.Kohel, eds., Springer-Verlag, Berlin, 372-389 (2002). |
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[79]
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(with Mats N‥aslund and I. Shparlinski) Hidden number problem with the trace and bit security of XTR and LUC, Lect. Notes in Comp. Sci. 2442, Springer-Verlag, Berlin, 433–448 (2002). |
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[80]
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Ramanujan hypergraphs, GAFA, Geom. funct. anal., vol. 14 (2004), 380-399. |
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[81]
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Ramanujan graphs and Ramanujan hypergraphs, IAS/Park City MathematicsSeries, to appear. |
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[82]
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Modularity of asymptotically optimal towers of function fields, Progress in Computer Science and Applied Logic, vol. 23, Birkh‥auser Verlag, Basel, 51-65 (2004). |
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[83]
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Character sums over norm groups, Finite Fields Appl. 12 (2006), 1-15. |
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[84]
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(joint with Ling Long and Zifeng Yang) On Atkin-Swinnerton-Dyer congruence relations, Journal of Number Theory, 113 (2005), 117-148. |
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[85]
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(joint with Ralf Koetter, Pascal O. Vontobel, and Judy Walker) Pseudo-Codewords of cycle codes via zeta functions, Proc. IEEE Information TheoryWorkshop, San Antonio, TX, USA, Oct. 24-29, 2004, 7-12. |
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[86]
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(joint with Ling Long and Zifeng Yang) Modular forms for noncongruence subgroups, Quaterly Journal of Pure and Applied Math., vol 1, No. 1, 205-221, 2005. |
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[87]
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(joint with Yotsanan Meemark) Ramanujan graphs on cosets of PGL2(Fq), Finite Fields Appl., 11 (2005), 511-543. |
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[88]
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(joint with Ralf Koetter, Pascal O. Vontobel, and Judy Walker) Characterizations of pseudo-codewords of LDPC codes, preprint, 2005. |
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[89]
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(joint with A. O. L. Atkin and L. Long) On Atkin and Swinnerton-Dyer congruence relations (2), preprint, 2005. |
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[90]
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Upper and lower bounds for A(q). In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear. |
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[91]
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Elkies’ modularity conjecture. In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear. |
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[92]
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Improved algebraic geometry bounds. In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear. |