• Corpus ID: 239016568

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

@inproceedings{Kaneko2021MotohashisFF,
title={Motohashi's Formula for the Fourth Moment of Individual Dirichlet \$L\$-Functions and Applications},
author={Ikuya Kaneko},
year={2021}
}
• I. Kaneko
• Published 18 October 2021
• Mathematics
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 C-aspect to the cubic moment of central !-values of Hecke–Maaß newforms of level at most @ and primitive central character k averaged over all primitive nonquadratic characters kmodulo @. Our formulæ would be viewed as reverse versions of recent work of Petrow…
1 Citations
Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions
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

## References

SHOWING 1-10 OF 77 REFERENCES
The Second Moment of the Product of the Riemann Zeta and Dirichlet $L$-Functions
We establish Motohashi’s formula for the second moment of the product of the Riemann zeta function and a Dirichlet !-function associated to an arbitrary primitive Dirichlet character modulo @ ∈ N. If
Motohashi’s fourth moment identity for non-archimedean test functions and applications
• Mathematics
Compositio Mathematica
• 2020
Motohashi established an explicit identity between the fourth moment of the Riemann zeta function weighted by some test function and a spectral cubic moment of automorphic $L$-functions. By an
The Riemann Zeta-Function and Hecke Congruence Subgroups. II
This is a rework of our old file, which has been left unpublished since September 1994, on an explicit spectral decomposition of the fourth power moment of the Riemann zeta-function against a weight
The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound.
• Mathematics
• 2019
We prove a Lindelof-on-average upper bound for the fourth moment of Dirichlet $L$-functions of conductor $q$ along a coset of the subgroup of characters modulo $d$ when $q^*|d$, where $q^*$ is the
A hybrid asymptotic formula for the second moment of Rankin–Selberg L-functions
• Mathematics
• 2012
Let g be a fixed modular form of full level, and let f j, k be a basis of holomorphic cuspidal newforms of even weight k, fixed level and fixed primitive nebentypus. We consider the Rankin-Selberg
Twelfth moment of Dirichlet L-functions to prime power moduli
• Mathematics
• 2019
We prove the q-aspect analogue of Heath-Brown's result on the twelfth power moment of the Riemann zeta function for Dirichlet L-functions to odd prime power moduli. Our results rely on the p-adic
Eisenstein series and the cubic moment for PGL(2)
Following a strategy suggested by Michel--Venkatesh, we study the cubic moment of automorphic $L$-functions on $\operatorname{PGL}_2$ using regularized diagonal periods of products of Eisenstein
On Motohashi's formula
We offer a new pespective of the proof of a Motohashi-type formula relating the fourth moment of $L$-functions for $\mathrm{GL}_1$ with the third moment of $L$-functions for $\mathrm{GL}_2$ over
LEVEL RECIPROCITY IN THE TWISTED SECOND MOMENT OF RANKIN–SELBERG $L$ -FUNCTIONS
• Mathematics
• 2018
We prove an exact formula for the second moment of Rankin–Selberg $L$ -functions $L(\frac{1}{2},f\times g)$ twisted by $\unicode[STIX]{x1D706}_{f}(p)$ , where $g$ is a fixed holomorphic cusp form
An explicit formula for the fourth power mean of the Riemann zeta-function
In the celebrated paper [1] Atkinson exhibited an explicit formula for the mean square of the Riemann zeta-function on the critical line, which greatly enriched the theory of this most fundamental