Quadratic twists of modular $L$-functions

Abstract: The behavior of quadratic twists of modular $L$-functions 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.

Mathematics

Audience: researchers in the topic

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