Title: On the poles of topological zeta functions
Authors: Lemahieu, Ann ×
Segers, Dirk
Veys, Willem #
Issue Date: 2006
Publisher: Amer mathematical soc
Series Title: Proceedings of the american mathematical society vol:134 issue:12 pages:3429-3436
Abstract: We study the topological zeta function Z(top), (f)(s) associated to a polynomial f with complex coefficients. This is a rational function in one variable, and we want to determine the numbers that can occur as a pole of some topological zeta function; by definition these poles are negative rational numbers. We deal with this question in any dimension. Denote P-n := {s(0) vertical bar there exists f is an element of C[x(1),..., x(n)] : Z(top,) (f) (s) has a pole in s(0)}. We show that {-( n- 1)/ 2-1/ i vertical bar i is an element of Z > (1)} is a subset of P-n; for n = 2 and n = 3, the last two authors proved before that these are exactly the poles less than -( n - 1)/2. As the main result we prove that each rational number in the interval [-( n- 1)/ 2, 0) is contained in P-n.
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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