Geodesic
Motohashi’s formula for the fourth moment of individual Dirichlet L-functions and applications
Forum of Mathematics, Sigma, Tome 10 (2022)

Voir la notice de l'article provenant de la source Cambridge University Press

A new reciprocity formula for Dirichlet L-functions associated to an arbitrary primitive Dirichlet character of prime modulus q is established. We find an identity relating the fourth moment of individual Dirichlet L-functions in the t-aspect to the cubic moment of central L-values of Hecke–Maaß newforms of level at most $q^{2}$ and primitive central character $\psi ^{2}$ averaged over all primitive nonquadratic characters $\psi $ modulo q. Our formula can be thought of as a reverse version of recent work of Petrow–Young. Direct corollaries involve a variant of Iwaniec’s short interval fourth moment bound and the twelfth moment bound for Dirichlet L-functions, which generalise work of Jutila and Heath-Brown, respectively. This work traverses an intersection of classical analytic number theory and automorphic forms. 
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     author = {Ikuya Kaneko},
     title = {Motohashi{\textquoteright}s formula for the fourth moment of individual {Dirichlet} {L-functions} and applications},
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Ikuya Kaneko. Motohashi’s formula for the fourth moment of individual Dirichlet L-functions and applications. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.33

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