Dans ce court article, nous prouvons une version quantitative du théorème de Khintchine–Groshev avec des conditions de congruence. Notre argument repose sur un argument classique de Schmidt sur le comptage de points de réseau génériques, qui à son tour repose sur une certaine borne de variance sur l’espace des réseaux.
In this short paper we prove a quantitative version of the Khintchine–Groshev Theorem with congruence conditions. Our argument relies on a classical argument of Schmidt on counting generic lattice points, which in turn relies on a certain variance bound on the space of lattices.
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@article{JTNB_2021__33_1_261_0,
author = {Alam, Mahbub and Ghosh, Anish and Yu, Shucheng},
title = {Quantitative {Diophantine} approximation with congruence conditions},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {261--271},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {33},
number = {1},
year = {2021},
doi = {10.5802/jtnb.1161},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.1161/}
}
TY - JOUR AU - Alam, Mahbub AU - Ghosh, Anish AU - Yu, Shucheng TI - Quantitative Diophantine approximation with congruence conditions JO - Journal de théorie des nombres de Bordeaux PY - 2021 SP - 261 EP - 271 VL - 33 IS - 1 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.1161/ DO - 10.5802/jtnb.1161 LA - en ID - JTNB_2021__33_1_261_0 ER -
%0 Journal Article %A Alam, Mahbub %A Ghosh, Anish %A Yu, Shucheng %T Quantitative Diophantine approximation with congruence conditions %J Journal de théorie des nombres de Bordeaux %D 2021 %P 261-271 %V 33 %N 1 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.1161/ %R 10.5802/jtnb.1161 %G en %F JTNB_2021__33_1_261_0
Alam, Mahbub; Ghosh, Anish; Yu, Shucheng. Quantitative Diophantine approximation with congruence conditions. Journal de théorie des nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 261-271. doi : 10.5802/jtnb.1161. http://www.numdam.org/articles/10.5802/jtnb.1161/
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