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科学研究
RESEARCH
Differential equations satisfied by modular forms
时间  Datetime
2021-01-06 15:30 — 16:30
地点  Venue
Zoom APP()
报告人  Speaker
楊一帆
单位  Affiliation
台湾大学
邀请人  Host
费佳睿
备注  remarks
ID: 97529069804; password: 120205
报告摘要  Abstract

 A classical result known since the nineteenth century asserts that if F(z) is a modular form of weight k and t(z) is a nonconstant modular function on a Fuchsian subgroup of SL(2,R) of the first kind, then F(z), zF(z),... z^kF(z), as (multi-valued) functions of t, are solutions of a (k+1)-st order linear ordinary differential equations with algebraic functions of t as coefficients. This result constitutes one of the main sources of applications of modular forms to other branches of mathematics. In this talk, we will give a quick overview of this classical result and explain some of its applications in number theory.