ON DIRICHLET SERIES ASSOCIATED WITH POLYNOMIALS

Authors
CARLETTI E BRAGADIN GM
Citation
E. Carletti et Gm. Bragadin, ON DIRICHLET SERIES ASSOCIATED WITH POLYNOMIALS, Proceedings of the American Mathematical Society, 121(1), 1994, pp. 33-37
Citations number
8
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
121
Issue
1
Year of publication
1994
Pages
33 - 37
Database
ISI
SICI code
0002-9939(1994)121:1<33:ODSAWP>2.0.ZU;2-Y
Abstract
Let P(X) be a polynomial of degree N with complex coefficients and d1 , d2 two complex numbers with real part greater then -1. Consider the Dirichlet series associated with the triple (P(X), d1, d2). [GRAPHICS] 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 s imple poles at s = (N + 1 - k)/2, k = 0, 1, ... . Finally we apply our explicit formula to Minakshisundaram's zeta function of the three-dim ensional sphere.