foto dirk

Home Page of Dirk Segers


Work information
Job: Postdoctoral Fellow of the Fund for Scientific Research - Flanders (Belgium).
Fields of Research: Algebraic Geometry, Singularity Theory, applications in Number Theory
Specific Research Topics: Zeta Functions (Igusa, topological, motivic), polynomial congruences and exponential sums


Contact information
Address: University of Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven (Heverlee), Belgium
Electronic mail address: dirk.segers@wis.kuleuven.be
Web address: http://wis.kuleuven.be/algebra/segers/segers.htm


Publications
  • D. Segers, A round table problem, The Mathematical Gazette 88 (March 2004), 115-116. (dvi, ps, pdf)
  • D. Segers and W. Veys, On the smallest poles of topological zeta functions, Compositio Math. 140 (2004), 130-144. (dvi, ps, pdf)
  • D. Segers, On the smallest poles of Igusa's p-adic zeta functions, Mathematische Zeitschrift 252 (2006), 429-455. (dvi, ps, pdf)
  • D. Segers, Lower bound for the poles of Igusa's p-adic zeta functions, Mathematische Annalen 336 (2006), 659-669. (dvi, ps, pdf)
  • A. Lemahieu, D. Segers and W. Veys, On the poles of topological zeta functions, Proceedings of the AMS 134 (2006), 3429-3436. (dvi, ps, pdf)
  • D. Segers, A vanishing result for Igusa's p-adic zeta functions with character, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 735-754. (dvi, pdf)
  • D. Segers, L. Van Proeyen and W. Veys, The motivic zeta function and its smallest poles, Journal of Algebra 317 (2007), 851-866. (dvi, pdf)
  • D. Segers, The asymptotic behaviour of the number of solutions of polynomial congruences, preprint (2007), 6 pages. (dvi, pdf)
  • D. Segers and W.A. Zúñiga-Galindo, Exponential sums and polynomial congruences along p-adic submanifolds, preprint (2009), 14 pages. (pdf)

Ph.D. thesis
I obtained my Ph.D. in april 2004 under the supervision of Willem Veys. The title of my thesis (dvi, ps, pdf) is "Smallest poles of Igusa's and topological zeta functions and solutions of polynomial congruences". Chapter 1 is an introduction to Igusa's, topological and motivic zeta functions. Chapters 2,3 and 5 correspond to the first three papers above on zeta functions. Chapter 4 contains calculations to obtain a vanishing result for Igusa's zeta function with character.