We compute a collection of mixed moments of the Riemann-zeta function by means of an approximate functional equation for the product of zeta functions. As an application we provide estimates for three-dimensional exponential sums with monomials which are in some instances sharper than those stemming from approaches entailing the use of existing bounds pertaining to analogous sums.
Nous calculons une collection de moments mixtes de la fonction zêta de Riemann à l’aide d’une équation fonctionnelle approximative pour le produit des fonctions zêta. Comme application, nous fournissons des estimations pour des sommes exponentielles tridimensionnelles à phase monomiale qui sont dans certains cas plus précises que celles provenant des approches nécessitant l’utilisation des estimations existantes des sommes analogues.
Accepté le :
Publié le :
DOI : 10.5802/jtnb.1294
Mots-clés : Exponential sums, Riemann zeta function, moments of zeta
Javier Pliego 1
CC-BY-ND 4.0
@article{JTNB_2024__36_2_725_0,
author = {Javier Pliego},
title = {Estimates for a three-dimensional exponential sum with monomials},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {725--766},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {36},
number = {2},
year = {2024},
doi = {10.5802/jtnb.1294},
mrnumber = {4830948},
zbl = {07948983},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1294/}
}
TY - JOUR AU - Javier Pliego TI - Estimates for a three-dimensional exponential sum with monomials JO - Journal de théorie des nombres de Bordeaux PY - 2024 SP - 725 EP - 766 VL - 36 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1294/ DO - 10.5802/jtnb.1294 LA - en ID - JTNB_2024__36_2_725_0 ER -
%0 Journal Article %A Javier Pliego %T Estimates for a three-dimensional exponential sum with monomials %J Journal de théorie des nombres de Bordeaux %D 2024 %P 725-766 %V 36 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1294/ %R 10.5802/jtnb.1294 %G en %F JTNB_2024__36_2_725_0
Javier Pliego. Estimates for a three-dimensional exponential sum with monomials. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 2, pp. 725-766. doi : 10.5802/jtnb.1294. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1294/
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