Root number correlation bias of Fourier coefficients of modular forms

Abstract: In a recen 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.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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