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# Texas A&M Number Theory Seminar

##
Department of Mathematics

Milner 317

Wednesdays, 12:30-1:30 PM

### Ahmad El-Guindy

Texas A&M University

#### Wednesday, September 12

#### Milner 317, 12:30PM

**Title:**Fourier Expansions with Modular Form Coefficients

**Abstract:**For non-negative integers , let be the unique modular
function that is holomorphic on the upper half-plane and with Fourier
expansion
. Asai, Kaneko, and Ninomiya showed that

where as usual is the weight Eisenstein series and
is the unique normalized weight cusp form. In this talk we show how
to obtain similar formulas starting from any meromorphic modular form
of weight . (In this context the above formula corresponds to ). We also discuss generalizations to forms on groups of higher level
for which the underlying modular curve is hyperelliptic.