Root number correlation bias of Fourier coefficients of modular forms
Root number correlation bias of Fourier coefficients of modular forms

Nina Zubrilina, Princeton University
IAS  Simonyi Hall Seminar Room SH101
InPerson and Online Talk
In a recent machine learning based study, He, Lee, Oliver, and Pozdnyakov observed a striking oscillating pattern in the average value of the Pth 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 Lfunctions when split by root number.
In my talk, I will discuss this root number correlation bias when the average is taken over weight 2 modular newforms of all Galois orbit sizes simultaneously. I will point to a source of this phenomenon in this case and compute the correlation function exactly.