Quantitative Diophantine approximation with congruence conditions
Journal de Théorie des Nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 261-271.

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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DOI : https://doi.org/10.5802/jtnb.1161
Classification : 11N56,  14G42
@article{JTNB_2021__33_1_261_0,
     author = {Mahbub Alam and Anish Ghosh and Shucheng Yu},
     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 = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1161/}
}
Mahbub Alam; Anish Ghosh; Shucheng Yu. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1161/

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