Numerical evidence toward a 2-adic equivariant "main conjecture"

Details Numerical evidence toward a 2-adic equivariant "main conjecture" Numerical evidence toward a 2-adic equivariant "main conjecture"

2009-04-24

arxiv.org/abs/0904.3819v1

Mathematics

Number Theory

Scientific paper

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.

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