Wen-Ch'ing Winnie Li





   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


   Automorphic Forms, Number Theory, Representation Theory, Coding Theory and Graph Theory


   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


   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 díŽOrsay, 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



   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;



Newforms and functional equations, Math. Ann. 212, 285-315 (1975)


On modular functions in characteristic p, Trans. Amer. Math. Soc. 246, 231-259 (1978)


(with A.O.L. Atkin) Twists of newforms and pseudo-eigenvalues of W-operators, Invent, Math. 48, 221-243 (1978)


Eisenstein series and decomposition theory over function fields, Math. Ann. 240, 115-139 (1979)


L-series of Rankin type and their functional equations, Math. Ann. 244, 135-166 (1979)


On the representations of GL(2), Part I: "-factors and n-closeness, J. reine ang. Math. 313, 27-42 (1980)


On the representations of GL(2), Part II: "-factors of the representations of GL(2) íĐ GL(2), J. reine ang. Math. 314, 3-20(1980)


(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)


Hecke-Weil-Jacquet-Langlands theorem revisited. In: Lectures Notes in Math. 751, 206-220, Springer-Verlag, N. Y. (1979)


Une caracterisation des representations automorphes de GL1 et GL2, C.R. Acad. Sci. Serie A 29, 681-684 (1980)


(with G. Harder and J. Weisinger) Dimensions of spaces of cusp forms over function fields, J. reine ang. Math. 319, 73-103 (1980)


(with S.-Y. R. Li) On generators of ideals associated with unions of linear varieties, Bull. London Math. Soc. 13, 59-65 (1981)


On a theorem of Hecke-Weil-Jacquet-Langlands. In: Recent Progress in Analytic Number Theory, vol. 2, 119-152, Academic Press (1980)


(with S.-Y. R. Li) Independence numbers of graphs and generators of ideals, Combinatorica 1, 55-61 (1981)


(with E. Formanek and P. Halpin) The Poincare series of the ring of 2 íĐ 2 generic matrices, J. Alg. 69, 105-112 (1981)


On converse theorems for GL(2) and GL(1), Amer. J. Math. 103, no. 5, 851-885 (1981)


(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)


Generators for the ideal of polynomial identities satisfied by 2 íĐ 2 matrices, J. Alg. 74, no. 1, 2446-263 (1982)


(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)


(with J. Soto-Andrade) Barnes identities and representations of GL2. Part I: Finite field case, J. reine ang. Math. 344, 171-179 (1983)


Barnes identities and representations of GL2. Part II: Nonarchimedean local field case, J. reine ang. Math. 345, 69-92 (1983)


Determination of the residue classes of a polynomial at integral arguments, Disc. Math. 47, 83-90 (1983)


Diagonalizing modular forms, J. Alg. 99, no. 1, 210-231 (1986)


(with B. Z. Moroz) On ideal classes of number fields containing integral ideals of equal norms, J. Number Theory 21, 185-203 (1985)


A criterion for automorphic representations of GL(1) and GL(2), SíŽem. de ThíŽeorie des Nombres de Bordeaux, 1982-83, exposíŽe no. 7 (1984)


(with P. GíŽerardin) Fourier transforms of representations of quaternions, J. reine ang. Math. 359, 121-173 (1985)


A criterion on automorphic forms for GL1 and GL2 over global fields. In: SíŽem. de ThíŽeorie des Nombres de Paris 1982-83, Progress in Math., vol. 51, 161-172, Birkhauser, Boston (1984)


(with P. GíŽerardin) A functional equation for degree two local factors, Canad. Math. Soc. Bull., vol. 28(3), 355-371 (1985)


(with P. GíŽerardin) Establishing correspondences without the trace formula, AMS Contemporary Math. 53, 185-200 (1986)


Various aspects of BarnesíŽ identity. In: SíŽem. de ThíŽeorie des Nombres de Paris 1984-85, Progress in Math., vol. 63, 187-203, Birkhauser, Boston (1986)


(with P. GíŽerardin) Identities on degree two local factors. In: Proceedings of the conference on íĘRepresentation Theory and Number Theory in connection with Local Langlands ConjectureíĘ, held at Irsee, West Germany, Dec. 15-20, 1985, in AMS Contemporary Math. 86 (1989), 225-248


(with P. GíŽerardin) Identities on quadratic Gauss sums, Transactions Amer. Math. Soc., vol. 321, no. 1, 159-182 (1990)


(with P. GíŽerardin) Degree two monomial representations of local Weil groups, J. fíLur reine und angewandt Math. 394 (1989), 1-30


On quadratic Gauss sums over local fields. In : SíŽem. de ThíŽeorie des Nombres de Paris 1985-86, Progress in Math., vol. 71, 133-145, Birkhauser, Boston (1987)


(with P. GíŽerardin) Functional equations and periodic sequences, in: ThíŽeorie 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)


(with P. GíŽerardin) Twisted Dirichlet series and distributions, CompositioMathematica 73, 271-293 (1990)


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


On local exceptional representations of GL(2), preprint


On local modular representations of GL(2), preprint


(with A. Harnchoowong) Sylow subgroups of ideal class groups with moduli, J. Number Theory, vol. 36, no. 3, 354-372 (1990)


Character sums and abelian Ramanujan graphs, J. Number Theory 41 (1992), 199-214


(with K. Feng) Eigenvalues of regular directed graphs, Appendix to no. 41, J. Number Theory 41 (1992), 214-217


(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


(with F. K. Hwang) Reliabilities of double loop networks, Prob. Eng. and Info. Sci. 5 (1991), 255-272.


Ideal class groups and Galois modules. In: SíŽeminaire de ThíŽeorie des Nombres Paris 1989-90, Progress in Math., 163-176, Birkhauser, Boston, Basel, Berlin, 1992.


(with X.-D. Hu and F. K. Hwang) Most reliable double loop networks in survival reliability, Network, vol. 23 (1993), 451-458.


(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.


(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.


(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.


(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.


(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.


Number-theoretic constructions of Ramanujan graphs. In: Columbia University Number Theory Seminar, New York 1992, AstíŽerisque, vol. 228 (1995), Soc. Math. de France, 101-120.


(with Keqin Feng) Spectra of hypergraphs and applications, J. Number Theory, vol. 60 (1996), 1-22.


Number Theory with Applications (book), World Scientific, Singapore-New Jersey -London-Hong Kong, 1996.


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


(with P. SolíŽe) Spectra of regular graphs and hypergraphs and orthogonal polynomials, European Journal of Combinatorics, vol. 17 (1996). 461-477.


European Journal of Combinatorics, vol. 17 (1996). 461-477. 57. (with S. Burr, P. ErdíLos and R. L. Graham) Complete sequences of sets of integer powers, Acta Arithmetica 77, vol. 2 (1996), 133-138.


(with M-K Leu) On the series for L(1,), Nagoya Math. J., vol. 141 (1996), 125-142.


(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.


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.


Character sums over p-adic fields, Journal of Number Theory, vol. 74, 181-229 (1999).


Geometry, graph theory and number theory. In: Algebra and Geometry (Taipei 1995), 83-102, Lect. Alg. Geom. 2, Internat. Press, Cambridge, MA. 1998.


(with B. Gao, F. Hwang and U. Rothblum) Partition-polytopes over 1-dimensional points, Mathematical Programming 85 (1999), no. 2, Ser. A, 335-362.


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).


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.


Eigenvalues of Ramanujan graphs. In: Emerging Applications of Number Theory (Minneapolis, MN, 1996), 387-403, IMA Vol. Math. Appl. 109, Springer, New York, 1999.


(with Ching-Li Chai) Function fields: arithmetic and applications, Contemporary Math. 245, 189-199 (1999)


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.


(with Xuning Feng) On Z4 codes with large Lee weight, preprint.


(with Hiren Maharaj) Coverings of curves with asymptotically many rational points, Journal of Number Theory 96, 232-256 (2002).


Various constructions of good codes. Contemporary Math., vol. 264, 271-285, (2000).


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.


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.


(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.


(with C.-L. Chai) Character sums, automorphic forms, equidistribution, and Ramanujan graphs, Part II. Eigenvalues of Terras graphs, Forum Math. 16 (2004), 631-661.


The arithmetic of modular forms, IAS/Park City Mathematics Series Volume 9, Arithmetic Algebraic Geometry, 479-504, 2001.


On negative eigenvalues of regular graphs, C. R. Acad. Sci. Paris, t. 333, SíŽerie I, 907-912, 2001.


(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).


(with Mats NíLaslund 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, 433íV448 (2002).


Ramanujan hypergraphs, GAFA, Geom. funct. anal., vol. 14 (2004), 380-399.


Ramanujan graphs and Ramanujan hypergraphs, IAS/Park City MathematicsSeries, to appear.


Modularity of asymptotically optimal towers of function fields, Progress in Computer Science and Applied Logic, vol. 23, BirkhíLauser Verlag, Basel, 51-65 (2004).


Character sums over norm groups, Finite Fields Appl. 12 (2006), 1-15.


(joint with Ling Long and Zifeng Yang) On Atkin-Swinnerton-Dyer congruence relations, Journal of Number Theory, 113 (2005), 117-148.


(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.


(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.


(joint with Yotsanan Meemark) Ramanujan graphs on cosets of PGL2(Fq), Finite Fields Appl., 11 (2005), 511-543.


(joint with Ralf Koetter, Pascal O. Vontobel, and Judy Walker) Characterizations of pseudo-codewords of LDPC codes, preprint, 2005.


(joint with A. O. L. Atkin and L. Long) On Atkin and Swinnerton-Dyer congruence relations (2), preprint, 2005.


Upper and lower bounds for A(q). In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear.


ElkiesíŽ modularity conjecture. In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear.


Improved algebraic geometry bounds. In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear.

[ Chinese  ]