Asymptotics of certain double series in Eulerian form
Abstract
We examine the asymptotic behavior of FA,B(q):=∑n=(rs)t∈ℤ2≥0q12ntAn+Bn(q)r(q)s, where A=(a1a2a2a1), B=(b1 b2), and a1, a2, b1, b2 are rational numbers satisfying some conditions while ntAn is not necessarily positive-definite. As an application, we obtain non-modularities of certain double-sum Eulerian series.
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