Abstract
Motivated by analytic number theory, we explore remainder versions of Ikehara’s Tauberian theorem yielding power law remainder terms. More precisely, for \(f:[1,\infty )\rightarrow {\mathbb R}\) non-negative and non-decreasing we prove \(f(x)-x=O(x^\gamma )\) with \(\gamma <1\) under certain assumptions on f. We state a conjecture concerning the weakest natural assumptions and show that we cannot hope for more.
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Communicated by Jens Funke.
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Müger, M. On Ikehara type Tauberian theorems with \(O(x^\gamma )\) remainders. Abh. Math. Semin. Univ. Hambg. 88, 209–216 (2018). https://doi.org/10.1007/s12188-017-0187-0
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DOI: https://doi.org/10.1007/s12188-017-0187-0