The fourth moment of individual Dirichlet L-functions on the critical line

Topacogullari, Berke

doi:10.1007/s00209-020-02610-9

Cited by 10 publications

(16 citation statements)

References 36 publications

(56 reference statements)

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“…We leave such pursuits and their applications to future work. Finally, Topaçoğullari [65] has manifested an asymptotic formula for the fourth moment of individual Dirichlet -functions. Via the specialisation of the test function in Theorem 1.1 and a sequence of standard manipulations such as spectral large sieve inequalities, one may arrive at an asymptotic formula of the same quality.…”

Section: Theorem 11 Let Be a Primitive Character Modulo A Prime And Letmentioning

confidence: 99%

“…We omit the proof of Corollary 1.8 since our method is quite analogous to that of Topaçoğullari [65]. Improving upon the error term in (1.11) in the -aspect requires some additional manoeuvres.…”

Section: Theorem 11 Let Be a Primitive Character Modulo A Prime And Letmentioning

confidence: 99%

“…This kind of sum has naturally arisen in the antecedent works such as [62,65,67] and ( ) ought to be replaced with the divisor function ( ) in our proof due to the convergence issue. One sifts out the congruence conditions on the right-hand side of (1.12) in terms of additive characters.…”

Section: Theorem 11 Let Be a Primitive Character Modulo A Prime And Letmentioning

confidence: 99%

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Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications

Kaneko

2021

Preprint

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A. A new reciprocity formula for Dirichlet -functions associated to an arbitrary primitive Dirichlet character of prime modulus is established. We find an identity relating the fourth moment of individual Dirichlet -functions in the -aspect to the cubic moment of central -values of Hecke-Maaß newforms of level at most 2 and primitive central character 2 averaged over all primitive nonquadratic characters modulo . Our formulae would be viewed as reverse versions of recent work of Petrow-Young. Direct corollaries include a version of Iwaniec's short interval fourth moment bound and the twelfth moment bound for individual Dirichlet -functions, which generalise work of Jutila and Jutila-Motohashi, respectively. This work traverses an intersection of analytic number theory and automorphic forms.

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Section: Theorem 11 Let Be a Primitive Character Modulo A Prime And Letmentioning

confidence: 99%

Section: Theorem 11 Let Be a Primitive Character Modulo A Prime And Letmentioning

confidence: 99%

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Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications

Kaneko

2021

Preprint

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“…It greatly enhances our understanding of the fourth moment of the ζfunction. There are also the recent works of Topacogullari [To21] and Kaneko [Ka21+] extending Motohashi's work to Dirichlet L-functions.…”

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confidence: 99%

Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions

Kwan¹

2021

Preprint

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Spectral moment formulae of various shapes have proven to be very successful in studying the statistics of central L-values. In this article, we establish, in a completely explicit fashion, such formulae for the family of GLp3q ˆGLp2q Rankin-Selberg L-functions using the period integral method. The Kuznetsov and the Voronoi formulae are not needed in our argument. We also prove the essential analytic properties and explicit formulae for the integral transform of our moment formulae. It is hoped that our method will provide insights into moments of L-functions for higher-rank groups.

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“…Watt, in [W13], gave an estimate analogous to Motohashi's result in [M07]. Topacogullari computed an asymptotic formula for Hecke L-functions in [To19]. Thorner also considered the fourth moment of Hecke L-functions and computed an upper bound in [Th19].…”

Section: Introductionmentioning

confidence: 96%

Automorphe Formen und L-Funktionen

Ulrike¹

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The fourth moment of individual Dirichlet L-functions on the critical line

Cited by 10 publications

References 36 publications

Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications

Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications

Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions

Automorphe Formen und L-Funktionen

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