Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 10.41, 30.00

Retrieve articles in all journals with MSC: 10.41, 30.00


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0260685-5
PII: S 0002-9947(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