Number Theory Seminar

Date: April 22, 2015

Time: 1:45PM - 2:45PM

Location: BLOC 220

Speaker: David Lowry-Duda, Brown University

Title: Bounding Sums of Fourier Coefficients of Modular Forms

Abstract: Understanding the sizes of Fourier coefficients of modular forms has been always been a central goal of the theory of modular forms. In this talk, we try to understand the size of the sum of the first several Fourier coefficients of full or half-weight forms. There is a Classical Conjecture analogous to the celebrated Ramanujan-Petersson conjecture, but it is not yet known in any case. We will show that the Classical Conjecture is true on average, and show how this result gives related results on sign changes. This talk is based on joint works with T. Hulse, C. Kuan, and A. Walker.