A Wiener-Ikehara type theorem and its application to Chebyshev bounds for Beurling primes

2026/02/28 by Yarne Tranoy, Jasson Vindas
Mathematics · #math.NT #math.CV

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Abstract

We provide a new version of the Wiener-Ikehara theorem where one deduces bounds 0< \liminf_x→∞ \fracS(x)e^x≤ \limsup_x→∞ \fracS(x)e^x <∞ for (in particular) a non-decreasing function S from a mild hypothesis on the boundary behavior of its Laplace transform on a vertical segment containing s=1. As an application, we establish new criteria for the validity of Chebyshev bounds for Beurling generalized prime number systems under weaker conditions than were known so far.

Citations

• Generalizations of Koga's version of the Wiener-Ikehara theorem
• Generalization of the effective Wiener-Ikehara theorem

Related

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• Quantitative version of Beurling-Helson theorem
• Generalization of the effective Wiener-Ikehara theorem
• Wiener's lemma along primes and other subsequences
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