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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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 PDF
Math. Comp. 84 (2015), 803-813 Request permission

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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Additional Information
  • Luis M. Navas
  • Affiliation: Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain
  • MR Author ID: 679507
  • ORCID: 0000-0002-5742-8679
  • Email: navas@usal.es
  • Francisco J. Ruiz
  • Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, Campus de la Plaza de San Francisco, 50009 Zaragoza, Spain
  • Email: fjruiz@unizar.es
  • Juan L. Varona
  • Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, Calle Luis de Ulloa s/n, 26004 Logroño, Spain
  • MR Author ID: 260232
  • ORCID: 0000-0002-2023-9946
  • Email: jvarona@unirioja.es
  • Received by editor(s): February 5, 2013
  • Received by editor(s) in revised form: July 28, 2013
  • Published electronically: August 19, 2014
  • Additional Notes: The authors were supported by grant MTM2012-36732-C03-02 of the DGI
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 803-813
  • MSC (2010): Primary 41A60; Secondary 11M35, 42A10
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02864-0
  • MathSciNet review: 3290964