Root Number Correlation Bias of Fourier Coefficients of Modular Forms

Abstract: In a recent study, He, Lee, Oliver, and Pozdnyakov observed a striking oscillating pattern in the average value of the P-th Frobenius trace of elliptic curves of prescribed rank and conductor in an interval range. Sutherland discovered that this bias extends to Dirichlet coefficients of a much broader class of arithmetic L-functions when split by rootnumber. In my talk, I will discuss this root numbercorrelation in families of holomorphic and Maass forms.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar