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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.