Title: On the holomorphy conjecture for igusas local zeta-function
Authors: Denef, Jan ×
Veys, Willem #
Issue Date: 1995
Publisher: Amer mathematical soc
Series Title: Proceedings of the american mathematical society vol:123 issue:10 pages:2981-2988
Abstract: To a polynomial f over a p-adic field K and a character chi of the group of units of the valuation ring of K one associates Igusa's local zeta function Z(s, f, chi), which is a meromorphic function on C. Several theorems and conjectures relate the poles of Z(s, f, chi) to the monodromy of f; the so-called holomorphy conjecture states roughly that if the order of chi does not divide the order of any eigenvalue of monodromy of f, then Z(s, f, chi) is holomorphic on C. We prove mainly that if the holomorphy conjecture is true for f(x(1),...,x(n-1)), then it is true for f(n(1),...,x(n-1)) + x(n)(k) with k greater than or equal to 3, and we give some applications.
ISSN: 0002-9939
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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