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<p>In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem. This approach avoids some verifications that are needed in Newman's path to the prime number theorem.</p>

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On the one-sided Ingham-Karamata Tauberian theorem

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • G. Debruyne

摘要

In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem. This approach avoids some verifications that are needed in Newman's path to the prime number theorem.