Number Theory Seminar

Local and global biases of modular forms

Kimball Martin, Professor, Department of Mathematics, Osaka Metropolitan University and University of Oklahoma,

Several years ago, the speaker observed that root numbers of modular (new)forms are biased toward +1. First I will discuss this and analogous local biases for the ramified components of modular forms. Part of this is joint work with Andrew Knightly. Then the speaker will discuss how local and global root numbers are correlated with Fourier coefficients at unramified primes, which is a phenomenon now known as murmurations.

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