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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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: 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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DOI: https://doi.org/10.1090/S0002-9947-1970-0260685-5
Keywords: Dirichlet series, generalized Dirichlet series, identities, functional equation with $ \Gamma $-factors, Hecke's functional equation, Abel summation
Article copyright: © Copyright 1970 American Mathematical Society