Theses

I have studied the smallest poles of the topological zeta function and the smallest real parts of the poles of Igusa's p-adic zeta function. For n=2 and n=3, I obtained results by using an embedded resolution of singularities. I discovered that the smallest real part of a pole of Igusa's p-adic zeta function is related with the divisibility of the M_i by powers of p. I obtained a general theorem on the divisibility of the M_i by powers of p, which I used to obtain the optimal lower bound for the real part of a pole of Igusa's p-adic zeta function in arbitrary dimension n. I obtained this lower bound also for the topological zeta function by taking the limit.

https://tel.archives-ouvertes.fr/tel-00006134

Contributor : Dirk Segers <>

Submitted on : Sunday, May 23, 2004 - 9:52:54 PM

Last modification on : Thursday, February 25, 2021 - 9:46:03 AM

Long-term archiving on: : Friday, April 2, 2010 - 8:22:24 PM

Contributor : Dirk Segers <>

Submitted on : Sunday, May 23, 2004 - 9:52:54 PM

Last modification on : Thursday, February 25, 2021 - 9:46:03 AM

Long-term archiving on: : Friday, April 2, 2010 - 8:22:24 PM