Quadratic twists of modular L-functions

Quadratic twists of modular L-functions

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Xiannan Li, Kansas State University

Online Talk

Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits. 

The behavior of quadratic twists of modular L-functions is at the critical point is related both to coefficients of half integer  weight modular forms and data on elliptic curves.  Here we describe a proof of an asymptotic for the second moment of this family of L-functions, previously available conditionally on the Generalized Riemann Hypothesis by the work of Soundararajan and Young.  Our proof depends on deriving an optimal large sieve type bound.