Complete asymptotic expansions associated with Epstein zeta-functions. II
Let \(s=\sigma+it\) be a complex variable, \(\sigma>1\), \(z=x+iy\) a complex parameter in the upper half-plane, \(a, b, \mu,\) and \(\nu\) real parameters, \(Q(u,v)\) a real positive-definite quadratic form. The author studies the corresponding generalized Epstein zeta function attached to the form \(Q\), in the case the quadratic form \(Q=|u+vz|^2\). Namely, he studies the asymptotic aspects of the zeta function when \(y\rightarrow+\infty\) and \(z\rightarrow0\) through the sector \(0<\)arg\(z<\pi\) and also studies definite asymptotic aspects of the Riemann-Liouville transform of the zeta function constructed in a particular case. For Part I see [ibid. 14, No. 2, 249--275 (2007; Zbl 1171.11023)].
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