On the distribution of zeros of the Hurwitz zeta-function |
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Authors: | Ramunas Garunkstis Jö rn Steuding. |
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Affiliation: | Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania ; Institut für Mathematik, Würzburg University, Am Hubland, 97074 Würzburg, Germany |
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Abstract: | Assuming the Riemann hypothesis, we prove asymptotics for the sum of values of the Hurwitz zeta-function taken at the nontrivial zeros of the Riemann zeta-function when the parameter either tends to and , respectively, or is fixed; the case is of special interest since . If is fixed, we improve an older result of Fujii. Besides, we present several computer plots which reflect the dependence of zeros of on the parameter . Inspired by these plots, we call a zero of stable if its trajectory starts and ends on the critical line as varies from to , and we conjecture an asymptotic formula for these zeros. |
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Keywords: | |
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