The functional equation of some Dirichlet series
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- by Bruce C. Berndt PDF
- Proc. Amer. Math. Soc. 29 (1971), 457-460 Request permission
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
- Tom M. Apostol, Dirichlet $L$-functions and character power sums, J. Number Theory 2 (1970), 223–234. MR 258766, DOI 10.1016/0022-314X(70)90022-3
- Harold Davenport, Multiplicative number theory, Lectures in Advanced Mathematics, No. 1, Markham Publishing Co., Chicago, Ill., 1967. Lectures given at the University of Michigan, Winter Term, 1966. MR 0217022
- Paul Epstein, Zur Theorie allgemeiner Zetafunktionen. II, Math. Ann. 63 (1906), no. 2, 205–216 (German). MR 1511399, DOI 10.1007/BF01449900 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.
- H. M. Stark, $L$-functions and character sums for quadratic forms. I, Acta Arith. 14 (1967/68), 35–50. MR 227122, DOI 10.4064/aa-14-1-35-50
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 457-460
- MSC: Primary 10.41
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276181-1
- MathSciNet review: 0276181