University of Oklahoma
When
2 – 3 p.m., Dec. 10, 2024
Where
Title: Distributions of root numbers and Fourier coefficients of modular forms
Abstract: Root numbers are signs that determine symmetries of L-functions. While asymptotically root numbers are +1 half the time and -1 half the time, there is in fact a bias towards sign +1. Moreover, an unexpected correlation between root numbers and Fourier coefficients of modular forms, termed murmurations, was recently discovered. I will explain these phenomena, as well as analogues for local root numbers.