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Wiener–Ikehara theorems and the Beurling generalized primes

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Abstract

The Wiener–Ikehara theorem is classical. Here we prove a converse of the theorem with “if and only if” conditions. We also extend this theorem to cover upper estimates and lower estimates respectively. Significant applications of these theorems to the study of the Beurling generalized primes are introduced too.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL , 61801, USA

    Wen-Bin Zhang

  2. Department of Mathematics, University of the West Indies, Mona, Kingston 7, Jamaica

    Wen-Bin Zhang

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  1. Wen-Bin Zhang
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Correspondence to Wen-Bin Zhang.

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Communicated by J. Schoißengeier.

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Zhang, WB. Wiener–Ikehara theorems and the Beurling generalized primes. Monatsh Math 174, 627–652 (2014). https://doi.org/10.1007/s00605-013-0597-8

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  • DOI: https://doi.org/10.1007/s00605-013-0597-8

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