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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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:
  • Francisco J. Ruiz
  • Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, Campus de la Plaza de San Francisco, 50009 Zaragoza, Spain
  • Email:
  • 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:
  • 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:
  • MathSciNet review: 3290964