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Proceedings of the American Mathematical Society

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The functional equation of some Dirichlet series

Author: Bruce C. Berndt
Journal: Proc. Amer. Math. Soc. 29 (1971), 457-460
MSC: Primary 10.41
MathSciNet review: 0276181
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Abstract: The functional equation for two classes of Dirichlet series is established. These Dirichlet series involve primitive characters and can be regarded as generalizations of Dirichlet's L-functions or of Epstein's zeta-functions. One class is also a generalization of some series studied by Stark.

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

  • [1] Tom M. Apostol, Dirichlet L-functions and character power sums, J. Number Theory 2 (1970), 223-234. MR 0258766 (41:3412)
  • [2] Harold Davenport, Multiplicative number theory, Markham, Chicago, Ill., 1967. MR 36 #117. MR 0217022 (36:117)
  • [3] Paul Epstein, Zur Theorie allgemeiner Zetafunktionen. II, Math. Ann. 63 (1907), 205-216. MR 1511399
  • [4] Adolf Hurwitz, Einige Eigenschaften der Dirichlet'schen Funktionen $ F(s) = \sum {(D/n) \cdot 1/{n^s}} $, die bei der Bestimmung der Klassenanzahlen binärer quadratischer Formen auftreten, Z. Math. Phys. 27 (1882), 86-101.
  • [5] H. M. Stark, L-functions and character sums for quadratic forms. I, Acta Arith. 14 (1967/68), 35-50. MR 37 #2707. MR 0227122 (37:2707)

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Keywords: Epstein zeta-function, Dirichlet L-function, primitive character, functional equation, quadratic form
Article copyright: © Copyright 1971 American Mathematical Society

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