On<i>p</i>-adic<i>L</i>-functions and cyclotomic fields. II

Abstract

Let p be a prime. If one adjoins to Q all p n -th roots of unity for n = 1,2,3, …, then the resulting field will contain a unique subfield Q ∞ such that Q ∞ is a Galois extension of Q with Gal ( Q ∞ / Q ) Z p , the additive group of p -adic integers. We will denote Gal ( Q ∞ / Q ) by Γ . In a previous paper [6], we discussed a conjecture relating p -adic L -functions to certain arithmetically defined representation spaces for Γ . Now by using some results of Iwasawa, one can reformulate that conjecture in terms of certain other representation spaces for Γ . This new conjecture, which we believe may be more susceptible to generalization, will be stated below.

Locations

• Nagoya Mathematical Journal - View - PDF