Numerical evidence toward a 2-adic equivariant "main conjecture"
Number Theory
2009-04-27 v1
Abstract
Recently Ritter and Weiss introduced an equivariant "main conjecture" than generalizes and refines the Main Conjecture of Iwasawa theory. In this paper, we show that, for the prime 2 and a dihedral extension of order 8 over Q, this conjecture is equivalent to a congruence condition on the coefficients of a power series with 2-adic integral coefficients constructed using the 2-adic L-series associated to the extension. We then verify that this congruence condition holds for the first coefficients in a large number of examples.
Cite
@article{arxiv.0904.3819,
title = {Numerical evidence toward a 2-adic equivariant "main conjecture"},
author = {Xavier-François Roblot and Alfred Weiss},
journal= {arXiv preprint arXiv:0904.3819},
year = {2009}
}