February 23, 2005

Yuri Bilu

Title: Divisibility of class numbers

Abstract:

This is a joint work with Florian Luca. Let m>1 and n>2 be integers. We show that for any large X there exist >>X^a (totally real) number fields of degree n, of discriminant smaller than X, and with class number divisible by m. Here a=1/2m(n-1).

this extends to arbitrary n similar results of R. Murphy for n=2.