Asymptotics of certain double series in Eulerian form

Abstract

We examine the asymptotic behavior of [Formula: see text] where [Formula: see text], [Formula: see text], and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are rational numbers satisfying some conditions while [Formula: see text] is not necessarily positive-definite. As an application, we obtain non-modularities of certain double-sum Eulerian series.