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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Dirichlet series associated with polynomials
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by E. Carletti and G. Monti Bragadin PDF
Proc. Amer. Math. Soc. 121 (1994), 33-37 Request permission

Abstract:

Let $P(X)$ be a polynomial of degree N with complex coefficients and ${d_1},{d_2}$ two complex numbers with real part greater then $-1$. Consider the Dirichlet series associated with the triple $(P(X),{d_1},{d_2})$ \[ L(s) = \sum \limits _{n = 1}^\infty {\frac {{P(n)}}{{{{(n + {d_1})}^s}{{(n + {d_2})}^s}}}.} \] In this paper we get an explicit formula for $L(s)$ in terms of special functions which gives meromorphic continuation of $L(s)$ with at most simple poles at $s = (N + 1 - k)/2,k = 0,1, \ldots$ Finally we apply our explicit formula to Minakshisundaram’s zeta function of the three-dimensional sphere.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 33-37
  • MSC: Primary 11M35; Secondary 11M41, 58G26
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1179586-5
  • MathSciNet review: 1179586