Abstract:We construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).

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中文翻译：

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关于Wiener-Ikehara和Ingham-Karamata定理中没有余数：一种构造方法

摘要：我们构造了明确的反例，表明除了经典的外，Wiener-Ikehara定理和Ingham-Karamata定理中的任何余数都不可能在半平面（甚至是半平面）的附加解析连续假设下获得到整个复杂平面）。

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