Jonah Klein, Dimitris Koukoulopoulos, Simon Lemieux
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引用次数: 0
Abstract
A BSTRACT . Covering systems were introduced by Erd˝os in 1950. In the same article where he introduced them, he asked if the minimum modulus of a covering system with distinct moduli is bounded. In 2015, Hough answered affirmatively this long standing question. In 2022, Balister, Bollob´as, Morris, Sahasrabudhe and Tiba gave a simpler and more versatile proof of Hough’s result. Building upon their work, we show that there exists some absolute constant c > 0 such that the j -th smallest modulus of a minimal covering system with distinct moduli is (cid:54) exp( cj 2 / log( j + 1)) .
期刊介绍：
This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.
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