We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms and , where are fixed integers, are prime numbers and is an integer.
Nous montrons des formules asymptotiques dans des intervalles courts pour le nombre moyen de représentations des entiers de la forme et , où sont des entiers fixés, sont des nombres premiers et est un entier.
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1041
Keywords: Waring-Goldbach problem, Hardy–Littlewood method
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@article{JTNB_2018__30_2_609_0,
author = {Alessandro Languasco and Alessandro Zaccagnini},
title = {Short intervals asymptotic formulae for binary problems with prime powers},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {609--635},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {30},
number = {2},
year = {2018},
doi = {10.5802/jtnb.1041},
zbl = {1441.11261},
mrnumber = {3891329},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1041/}
}
TY - JOUR AU - Alessandro Languasco AU - Alessandro Zaccagnini TI - Short intervals asymptotic formulae for binary problems with prime powers JO - Journal de théorie des nombres de Bordeaux PY - 2018 SP - 609 EP - 635 VL - 30 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1041/ DO - 10.5802/jtnb.1041 LA - en ID - JTNB_2018__30_2_609_0 ER -
%0 Journal Article %A Alessandro Languasco %A Alessandro Zaccagnini %T Short intervals asymptotic formulae for binary problems with prime powers %J Journal de théorie des nombres de Bordeaux %D 2018 %P 609-635 %V 30 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1041/ %R 10.5802/jtnb.1041 %G en %F JTNB_2018__30_2_609_0
Alessandro Languasco; Alessandro Zaccagnini. Short intervals asymptotic formulae for binary problems with prime powers. Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 2, pp. 609-635. doi : 10.5802/jtnb.1041. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1041/
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