We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series.

Keywords:

Dirichlet series integrals, Hurwitz zeta functions, Plancherel theorems, L-series Dirichlet series integrals, Hurwitz zeta functions, Plancherel theorems, L-series

MSC Classifications:

11M35, 11M41, 30B50 show english descriptions Hurwitz and Lerch zeta functions
Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX] 11M35 - Hurwitz and Lerch zeta functions
11M41 - Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
30B50 - Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]

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