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arXiv · 0904.3819

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

Xavier-François Roblot·Alfred Weiss
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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.

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Xavier-François Roblot, Alfred Weiss. 2009-04-24. Numerical evidence toward a 2-adic equivariant "main conjecture". https://arxiv.org/abs/0904.3819

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