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arXiv · 1712.01681

Asymptotics to all orders of the Hurwitz zeta function

Arran Fernandez·Athanassios S. Fokas
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Abstract

We present several formulae for the large-$t$ asymptotics of the modified Hurwitz zeta function $\zeta_1(x,s),x>0,s=\sigma+it,0<\sigma\leq1,t>0,$ which are valid to all orders. In the case of $x=0$, these formulae reduce to the asymptotic expressions recently obtained for the Riemann zeta function, which include the classical results of Siegel as a particular case.

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Arran Fernandez, Athanassios S. Fokas. 2017-12-05. Asymptotics to all orders of the Hurwitz zeta function. https://doi.org/10.1016/j.jmaa.2018.05.012

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