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Nina Zubrilina, Princeton University

Root Number Correlation Bias of Fourier Coefficients of Modular Forms

4:00 pm–4:50 pm
Avery Hall Room: 115
Additional Info: AVH
Shah Roshan Zamir
In a recent machine learning-based 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 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.

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This event originated in Math.