Theoretical Statistics and Mathematics Unit, ISI 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.