Willem Veys
KU Leuven, Department of Mathematics, Faculty Member
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
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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... more
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 | \exists f in C[x_1,..., x_n] : Z_{top,f}(s) has a pole in s_0}. We show that {-(n-1)/2-1/i | i in 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 then -(n-1)/2. As main result we prove that each rational number in the interval [-(n-1)/2,0) is contained in P_n.
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Let F be a number field and f ∈ F (x1 ,... , xn) \ F.T o any completion K of F and any character κ of the group of units of the valuation ring of K one associates Igusa's local zeta function ZK(κ, f,... more
Let F be a number field and f ∈ F (x1 ,... , xn) \ F.T o any completion K of F and any character κ of the group of units of the valuation ring of K one associates Igusa's local zeta function ZK(κ, f, s). The holomorphy conjecture states that for all except a finite number of completions K
Research Interests:
Let (S; 0) be a normal surface germ and f a nonconstant regular function on (S; 0)with f(0) = 0. Using any additive invariant on complex algebraic varieties one canassociate a zeta function to these data, where the topological and motivic... more
Let (S; 0) be a normal surface germ and f a nonconstant regular function on (S; 0)with f(0) = 0. Using any additive invariant on complex algebraic varieties one canassociate a zeta function to these data, where the topological and motivic zeta functionare the roughest and the nest one, respectively. In this paper we are interested in ageometric determination of