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SUMMARY:YiFan Yang (National Taiwan University)
DTSTART:20210106T070000Z
DTEND:20210106T080000Z
DTSTAMP:20260423T041526Z
UID:numsjtu/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/numsjtu/4/">
 Differential equations satisfied by modular forms</a>\nby YiFan Yang (Nati
 onal Taiwan University) as part of SJTU number theory seminar\n\n\nAbstrac
 t\nA 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 $SL(2\,\\mathbb{R})$ 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 w
 ith 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 classica
 l result and explain some of its applications in number theory.\n
LOCATION:https://researchseminars.org/talk/numsjtu/4/
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