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

    ROR https://ror.org/02f40zc51

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Mathematics of Computation

ISSN: 0025-5718

Year of publication: 2015

Volume: 84

Issue: 292

Pages: 803-813

Type: Article

More publications in: Mathematics of Computation

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.