Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function

Navas, Luis; Ruiz, Francisco; Varona, Juan

doi:10.1090/S0025-5718-2014-02864-0

Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function
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by Luis M. Navas, Francisco J. Ruiz and Juan L. Varona;

Math. Comp. 84 (2015), 803-813

DOI: https://doi.org/10.1090/S0025-5718-2014-02864-0

Published electronically: August 19, 2014

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Abstract:

The Lindelöf-Wirtinger expansion of the Lerch transcendent function implies, as a limiting case, Hurwitz’s formula for the eponymous zeta function. A generalized form of Möbius inversion applies to the Lindelöf-Wirtinger expansion and also implies an inversion formula for the Hurwitz zeta function as a limiting case. The inverted formulas involve the dynamical system of rotations of the circle and yield an arithmetical functional equation.

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