Number Theory & Representation Theory Day

國立成功大學數學系   國家理論科學研究中心數學組

共同主辦
Speakers :
                Prof. Tong Hai Yang 楊同海    (University of Wisconsin)
                Prof. V. Maillot                               (University Paris 7)
                Prof. Chia Fu Yu         余家富   (Columbia University)
                Prof. Chian-Jen Wang 王千真   (University of Minnesota)
                Prof. Shu-Yen Pan       潘戍衍    (National Cheng Kung University)

Place :    Lecture Room, Department of Mathematics
                National Cheng Kung University, Tainan
Time Speaker Topic

10:30 - 11:30

Tong- Hai Yang

Number Fields and Modular Forms

11:40 - 12:30

V. Maillot

Quadrilatera, elliptic curves and computing Mahler measure

14:00 - 15:00

Chia Fu Yu

Hecke Orbit Problems and special points

15:10 - 16:10

Chian-Jen Wang

Certain Distinguished Representations on the Metaplectic Groups

16:30 - 17:30

Shu-Yen Pan

Local theta correspondence of supercuspidal representations

Let F be a totally real number field of degree d and let K be a totally imaginary quadratic extension of F. For an even integer k, Hecke constructed an Hilbert modular form of weight k by means of Eisenstein series in 1924. In 1969, Siegel restricted these Eisenstein series diagonally to the upper half plane to obtain interesting elliptic  modular forms (the usual modular form) of weight dk and use them to compute the value of Dedekind zeta functions at  negative integers among others. In fact, when F is real quadratic,  Hecke also constructed Eisenstein series of weight one (using the so-called Hecke's trick). Unfortunately, he messed up with signs, and the form he constructed in the end is identically zero. Zagier siezed this fact to study singular moduli with Gross. In this talk, we will explain that a simple modification of Hecke's idea would produce a lot of honest non-zero Hilbert modular forms and thus a lot of elliptic modular forms by restricting diagonally.