p-adic measures associated with zeta values and p-adic \log\n multiple gamma functions

2017/04/15 by Tomokazu Kashio, Kashio, Tomokazu
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11R27 #11R37 #11R42 #11R80 #11S40 #11S80 #33B15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1704.04606

openalex publication_date 2017/04/15 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study a relation between two refinements of the rank one abelian\nGross-Stark conjecture: For a suitable abelian extension H/F of number\nfields, a Gross-Stark unit is defined as a p-unit of H satisfying some\nproporties. Let \τ \∈ \Gal(H/F). Yoshida and the author\nconstructed the symbol Y_p(\τ) by using p-adic \log multiple gamma\nfunctions, and conjectured that the \log_p of a Gross-Stark unit can be\nexpressed by Y_p(\τ). Dasgupta constructed the symbol u_T(\τ) by using\nthe p-adic multiplicative integration, and conjectured that a Gross-Stark\nunit can be expressed by u_T(\τ). In this paper, we give an explicit\nrelation between Y_p(\τ) and u_T(\τ).\n

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