# Seminar at SMU Delhi

May 28, 2014 (Wednesday) , 3:30 PM at Webinar
Speaker: Narasimha Kumar, IIT, Hyderabad
Title: On the algebraicity of the Fourier coefficients of half-integral weight modular forms
Abstract of Talk
It is well-known that a normalized Hecke eigenform of integral weight has algebraic Fourier coefficients. Moreover, there exists a number field containing all these. However, for half-integral weight modular forms, there are no analogous results known. In a joint work with Soma Purkait, we show that the algebraicity of the Fourier coefficients of half-integral weight modular forms can be determined by checking the algebraicity of the first few of them. We also give a necessary and sufficient condition for a half-integral weight modular form to be in Kohnen’s +-subspace by considering only finitely many terms.