On Stickelberger Elements for ℚ(ζ_pⁿ⁺¹)⁺ and p-adic L-functions

2015/09/22 by Timothy All, All, Timothy
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.NT

paper · pdf · doi:10.48550/arxiv.1509.06441

arxiv created 2015/09/22 · arxiv updated 2015/09/23

Abstract

We give a survey of a couple known constructions of p-adic L-functions including Iwasawa's construction from classical Stickelberger elements. We then construct "real" Stickelberger elements, i.e., explicit elements in the Galois group ring with ℤ_p coefficients that annihilate the Sylow p-subgroup of the ideal class group of ℚ(ζ_pⁿ⁺¹)⁺. In analogy with Iwasawa's work, we show that these elements are coherent in ℤ_p-towers and give rise to twisted p-adic L-functions.

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