Steve Lester: Signs of Fourier coefficients of half-integral weight modular forms

Time: Wed 2019-08-21 11.00

Lecturer: Steve Lester, Queen Mary University, London

Location: F11,

Fourier coefficients of half-integral weight modular forms
encode arithmetic information. For instance given a square-free
integer n, a theorem of Walspurger shows the square of the nth Fourier
coefficient of a half-integral weight form is proportional to the
central value of an L-function. The signs of these Fourier
coefficients remain mysterious. In this talk, I will discuss recent
joint work with Maksym Radziwill (CalTech) in which we detect sign
changes along the sequence of Fourier coefficients of half-integral
weight forms.
 

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