An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions

Autores: Masanori Katsurada
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 48, Fasc. 1-2, 1997, págs. 137-154
Idioma: inglés
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Resumen
- We shall establish full asymptotic expansions for the mean squares of Lerch zetafunctions, in the form (1.1) and (1.2) given below, based on F. V. Atkinson’s device (cf. [2], [4, Chapter 15] and [5, Chapter 2]). Mellin-Barnes’ type integral expression for an infinite double sum (see (3.2) and (3.5)) will play a central role in the derivation of our main formulae (2.1) and (2.2).