Identities involving the coefficients of a class of Dirichlet series. IV

Author:
Bruce C. Berndt

Journal:
Trans. Amer. Math. Soc. **149** (1970), 179-185

MSC:
Primary 10.41; Secondary 30.00

MathSciNet review:
0260685

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a class of Dirichlet series satisfying a functional equation with gamma factors. We define a generalized Dirichlet series that is analogous to the generalized zeta-function of Riemann. An analytic continuation for these generalized series is derived, and a few simple properties are established. Secondly, we prove a theorem on the Abel summation of Dirichlet series that satisfy Hecke's functional equation.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0260685-5

Keywords:
Dirichlet series,
generalized Dirichlet series,
identities,
functional equation with -factors,
Hecke's functional equation,
Abel summation

Article copyright:
© Copyright 1970
American Mathematical Society