Series: Mathematics Colloquium

Date: Thursday, April 11, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Winnie Li

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Ken Ono, University of Wisconsin

Title: Values of Modular Functions and Divisors of Modular Forms

Abstract: 

The values and the coefficients of the modular function j(z) play a
variety of important roles in number theory and representation theory.
For example, its values generate class fields in algebraic number
theory, and its coefficients are the degrees of the graded
representation of the Monster group.  In this lecture I will introduce
a specific sequence of modular functions j_n whose arithmetic
literally dictates the behavior of all modular forms on SL_2(Z) and
its congruence subgroups.  This is joint work with Jan Bruinier and
Winfried Kohnen.  The corollaries include: 1) Borcherds type infinite
products for generic forms; 2) Universal recursions for Fourier
expansions of all forms; 3) p-adic class number formulas.