Dans son article [5], W. M. Schmidt a obtenu une estimation de somme exponentielle pour les systèmes de polynômes sans polynômes linéaires, qui a ensuite été utilisée pour appliquer la méthode du cercle de Hardy–Littlewood. Nous démontrons une estimation analogue pour les systèmes qui incluent des polynômes linéaires.
In his paper [5], W. M. Schmidt obtained an exponential sum estimate for systems of polynomials without linear polynomials, which was then used to apply the Hardy–Littlewood circle method. We prove an analogous estimate for systems which include linear polynomials.
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DOI : 10.5802/jtnb.1035
Mots clés : Hardy–Littlewood circle method, exponential sum estimate
@article{JTNB_2018__30_2_485_0,
author = {Yamagishi, Shuntaro},
title = {An exponential sum estimate for systems with linear polynomials},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {485--499},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {30},
number = {2},
year = {2018},
doi = {10.5802/jtnb.1035},
mrnumber = {3891323},
zbl = {1443.11160},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/jtnb.1035/}
}
TY - JOUR AU - Yamagishi, Shuntaro TI - An exponential sum estimate for systems with linear polynomials JO - Journal de théorie des nombres de Bordeaux PY - 2018 SP - 485 EP - 499 VL - 30 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://archive.numdam.org/articles/10.5802/jtnb.1035/ DO - 10.5802/jtnb.1035 LA - en ID - JTNB_2018__30_2_485_0 ER -
%0 Journal Article %A Yamagishi, Shuntaro %T An exponential sum estimate for systems with linear polynomials %J Journal de théorie des nombres de Bordeaux %D 2018 %P 485-499 %V 30 %N 2 %I Société Arithmétique de Bordeaux %U http://archive.numdam.org/articles/10.5802/jtnb.1035/ %R 10.5802/jtnb.1035 %G en %F JTNB_2018__30_2_485_0
Yamagishi, Shuntaro. An exponential sum estimate for systems with linear polynomials. Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 2, pp. 485-499. doi : 10.5802/jtnb.1035. http://archive.numdam.org/articles/10.5802/jtnb.1035/
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