10 citations · 13 across the 9 of their papers we have counts for
9 papers
The asymptotic behaviour of the number of solutions of polynomial congruences
Dirk Segers
One mentions in a lot of papers that the poles of Igusa's p-adic zeta function determine the asymptotic behavior of the number of solutions of polynomial congruences. However, no p…
On the structure of the fibers of truncation morphisms
Helena Cobo Pablos, Dirk Segers
Let k be an algebraically closed field and let X be a separated scheme of finite type over k of pure dimension d. We study the structure of the fibres of the truncation morphisms f…
Determination of the real poles of the Igusa zeta function for curves
Denis Ibadula, Dirk Segers
The numerical data of an embedded resolution determine the candidate poles of Igusa's p-adic zeta function. We determine in complete generality which real candidate poles are actua…
Exponential Sums and Polynomial Congruences Along p-adic Submanifolds
Dirk Segers, W. A. Zuniga-Galindo
In this article, we consider the estimation of exponential sums along the points of the reduction mod of a -adic analytic submanifold of . More prec…
The motivic zeta function and its smallest poles
Dirk Segers, Lise Van Proeyen, Willem Veys
Let f be a regular function on a nonsingular complex algebraic variety of dimension d. We prove a formula for the motivic zeta function of f in terms of an embedded resolution. Thi…
Lower bound for the poles of Igusa's p-adic zeta functions
Dirk Segers
Let K be a p-adic field, R the valuation ring of K, P the maximal ideal of R and q the cardinality of the residue field R/P. Let f be a polynomial over R in n>1 variables and let χ…