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We study the second moment of the central values of quadratic twists of a modular $L$ -function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.

The shifted fourth moment of automorphic L-functions of prime power level

Olga Balkanova (2016)

Acta Arithmetica

We prove an asymptotic formula for the fourth moment of automorphic L-functions of level $p^{ν}$ , where p is a fixed prime number and ν → ∞. This is a continuation of work by Rouymi, who computed the asymptotics of the first three moments at a prime power level, and a generalization of results obtained for a prime level by Duke, Friedlander Iwaniec and Kowalski, Michel VanderKam.

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Taille des valeurs de fonctions L de carrés symétriques au bord de la bande critique.

The boundary of the Eisenstein symbol.

The boundary of the Eisenstein symbol (Erratum).

The critical order of vanishing of automorphic L-functions with large level.

The critical values of certain Dirichlet series.

The cubic moment of central values of automorphic $L$ -functions.

The L2-Lefschetz numbers of Hecke operators.

The l-adic representations attached to a certain noncongruence subgroup.

The L-function L3(s, ...) is entire.

The Modular Symbol and Continued Fractions in Higher Dimensions.

The p-adic L-functions attached to Rankin convolutions of modular forms.

The residual spectrum of $S p_{4}$

The second moment of quadratic twists of modular L-functions

The shifted fourth moment of automorphic L-functions of prime power level

The Spectral Mean Square of Hecke L-functions on the Critical Line

The Tamagawa number conjecture of adjoint motives of modular forms

The Theta Correspondence and Harmonic Forms. I.

The Theta Correspondence and Harmonic Forms. II.

The universal ordinary distribution

The Z/2 Z cohomology of the universal ordinary distribution

Currently displaying 1 – 20 of 23