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

Masanori Katsurada

• 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).