Riemann-Siegel integral formula for the Lerch zeta function

Eugenio P. Balanzario; Jorge Sánchez-Ortiz;

Abstract:

Here we present a Riemann-Siegel integral formula for the Lerch zeta function. Proceeding as in Turing's method for computing the Riemann zeta function, our integral formula allows for the numerical computation of the Lerch zeta function by numerical quadratures.

Keywords: Lerch zeta function; Riemann-Siegel; saddle point

MSC: 11M35

Journal: Mathematics of Computation

ISSN: 0025-5718

Year: 2012

Volume: 81

Number: 280

Pages: 2319--2333

Zbl Number: 1292.11097

MR Number: 2945158

Revision: 1

DOI: 10.1090/S0025-5718-2011-02566-4