Quantitative Diophantine approximation with congruence conditions
Mahbub Alam1; Anish Ghosh1; Shucheng Yu2
1 School of Mathematics Tata Institute of Fundamental Research Mumbai 400005, India
2 Department of Mathematics Uppsala University, Box 480 SE-75106, Uppsala, Sweden
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 261-271.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.1161
Classification: 11N56, 14G42

Mahbub Alam 1; Anish Ghosh 1; Shucheng Yu 2

1 School of Mathematics Tata Institute of Fundamental Research Mumbai 400005, India
2 Department of Mathematics Uppsala University, Box 480 SE-75106, Uppsala, Sweden
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Mahbub Alam; Anish Ghosh; Shucheng Yu. Quantitative Diophantine approximation with congruence conditions. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 261-271. doi : 10.5802/jtnb.1161. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1161/

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