Resumen: 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 M ¨obius 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. Idioma: Inglés DOI: 10.1090/S0025-5718-2014-02864-0 Año: 2015 Publicado en: MATHEMATICS OF COMPUTATION 84, 292 (2015), 803-813 ISSN: 0025-5718 Factor impacto JCR: 1.464 (2015) Categ. JCR: MATHEMATICS, APPLIED rank: 39 / 254 = 0.154 (2015) - Q1 - T1 Factor impacto SCIMAGO: 1.521 - Algebra and Number Theory (Q1) - Computational Mathematics (Q1) - Applied Mathematics (Q1)