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On zeta functions associated with polynomials

Published online by Cambridge University Press:  17 April 2009

Andrzej Dąbrowski
Andrzej Dąbrowski
Affiliation:
University of Szczecin, Institute of Mathematics, ul. Wielkopolska 15, 70-451 Szczecin, Poland, e-mail: dabrowsk@sus.univ. szczecin.pl
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Abstract

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We give direct proofs of meromorphic continuality on the whole complex plane of certain zeta functions ZP, Q (s) and Z (P/Q, s) associated with a pair of polynomials P, Q. We calculate ZP, Q (−q) (q a non-negative integer) and give explicit formulas for the residues of Z (P/Q, s) at poles.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 455 - 458
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Carletti, E. and Bragadin, G. Monti, ‘On Dirichlet series associated with polynomials, Proc. Amer. Math. Soc. 121 (1994), 33–37.CrossRefGoogle Scholar
[2]Eie, M., ‘On a Dirichlet series associated with a polynomial, Proc. Amer. Math. Soc. 110 (1990), 583–590.CrossRefGoogle Scholar
[3]Müller, H., ‘On generalized zeta-functions at negative integers, Illinois J. Math. 32 (1988), 222–229.CrossRefGoogle Scholar
[4]Sargos, P., ‘Prolongement méromorphe des séries de Dirichlet associées à des fractions rationnelles de plusieurs variables, Ann. Inst. Fourier 34 (1984), 83–123.CrossRefGoogle Scholar