Speaker: Nina Zubrilina (MIT)

TItle: 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 root number. In my talk, I will discuss this root number correlation in families of holomorphic and Maass forms.