Abstract
AbstractDirichlet series associated with the Poincaré series attached to $$\mathrm{SL}(2,{{\mathbb {Z}}})$$
SL
(
2
,
Z
)
are introduced. Integral representations and transformation formulas are given, which describe the Voronoï-type summation formula for the exponential-type generating function of the Riemann zeta-function. As an application, a new proof of the Fourier series expansion of holomorphic Poincaré series is given.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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