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Mollification of the fourth moment of Dirichlet $L$-functions

Volume 191 / 2019

Raphaël Zacharias Acta Arithmetica 191 (2019), 201-257 MSC: Primary 11M06; Secondary 11M26. DOI: 10.4064/aa170901-16-10 Published online: 16 September 2019

Abstract

We evaluate some twisted fourth moment of Dirichlet $L$-functions at the central point $s={1/2}$ and for prime moduli $q$. The principal tool is a careful analysis of a shifted convolution problem involving the divisor function using the spectral theory of automorphic forms. Having in mind simultaneous non-vanishing results, we apply our result to establish an asymptotic formula for a mollified fourth moment for this family of $L$-functions.

Authors

  • Raphaël ZachariasÉcole polytechnique fédérale de Lausanne
    route Cantonale
    1015 Lausanne, Switzerland
    e-mail

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