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Erratum: Limiting properties of the distribution of primes in an arbitrarily large number of residue classes

Part of: Zeta and $L$-functions: analytic theory Set functions and measures on spaces with additional structure Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  05 November 2020

Lucile Devin
Lucile Devin*
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, SE-412 96, Sweden
*
e-mail:devin@chalmers.se
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Abstract

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As pointed out by Alexandre Bailleul, the paper mentioned in the title contains a mistake in Theorem 2.2. The hypothesis on the linear relation of the almost periods is not sufficient. In this note, we fix the problem and its minor consequences on other results in the same paper.

Keywords

Chebyshev’s biasalmost-periodic functions

MSC classification

Primary: 11K70: Harmonic analysis and almost periodicity
Secondary: 28C15: Set functions and measures on topological spaces (regularity of measures, etc.) 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses
Type
Erratum
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 1041 - 1044
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Copyright
© Canadian Mathematical Society 2020

References

Bailleul, A., Explicit Kronecker-Weyl theorems and applications to prime number races . Preprint, 2020. http://arxiv.org/abs/2007.05763.Google Scholar
Devin, L., Limiting properties of the distribution of primes in an arbitrarily large number of residue classes. Canad. Math. Bull. 63(2020), 837–849. http://dx.doi.org/10.4153/S0008439520000089 CrossRefGoogle Scholar
Lang, S., Algebra. 3rd ed., Graduate Texts in Mathematics, 211, Springer-Verlag, New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0041-0Google Scholar