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

**Time: **
Wed 2019-08-21 11.00

**Location: **
F11,

**Participating: **
Steve Lester, Queen Mary University, London

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.