Nina Zubrilina: Murmurations of modular forms (NTWS 212)

Abstract: In a recent machine learning-based study, He, Lee, Oliver, and Pozdnyakov observed an unexpected 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 later discovered that this bias extends to Dirichlet coefficients of other classes of L-functions when split by root number. In my talk, I will prove this bias for a family of holomorphic modular forms and for a family of Maass forms.

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date:
Thursday, May 16, 2024 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, May 17, 2024 (1am AEST, 3am NZST)