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

  1. Navas, L.M. 1
  2. Ruiz, F.J. 2
  3. Varona, J.L. 3
  1. 1 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    GRID grid.11762.33

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    GRID grid.11205.37

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Journal:
Mathematics of Computation

ISSN: 0025-5718

Year of publication: 2015

Volume: 84

Issue: 292

Pages: 803-813

Type: Article

Export: RIS

Metrics

Cited by

  • Scopus Cited by: 2 (12-06-2021)

Journal Citation Reports

  • Year 2015
  • Journal Impact Factor: 1.464
  • Best Quartile: Q1
  • Area: MATHEMATICS, APPLIED Quartile: Q1 Rank in area: 39/254 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2015
  • SJR Journal Impact: 1.521
  • Best Quartile: Q1
  • Area: Algebra and Number Theory Quartile: Q1 Rank in area: 6/91
  • Area: Applied Mathematics Quartile: Q1 Rank in area: 61/545
  • Area: Computational Mathematics Quartile: Q1 Rank in area: 17/181

CiteScore

  • Year 2015
  • CiteScore of the Journal : 2.9
  • Area: Algebra and Number Theory Percentile: 96
  • Area: Applied Mathematics Percentile: 77
  • Area: Computational Mathematics Percentile: 75

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.