Abstract: Fix a polynomial f over the integers in an arbitrary number of variables. Studying the numbers of solutions of polynomial congruences f = 0 modulo m, for varying m, is a difficult number theoretical problem. We present an approach using on the one hand (p-adic) integration/Igusa-type zeta functions, and on the other hand algebraic geometry/resolution of singularities. There is also an intriguing conjectural relation with different topological properties of f, considered as map on complex affine space.
Polynomial congruences, Igusa-type zeta functions and resolution of singularities
07.04.2017 11:00 - 12:30
Organiser:
Ch. Chiu
Location: