v-adic periods of Carlitz motives and Chowla-Selberg formula revisited

2024/07/21 by Chieh-Yu Chang, Chang, Chieh-Yu, Fu‐Tsun Wei +3
Mathematics · #11J93 #11R58 #Advanced Mathematical Identities #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.15024

openalex publication_date 2024/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let v be a finite place of \mathbbF_q(θ). In this paper, we interpret v-adic arithmetic gamma values in terms of the v-adic crystalline-de Rham periods of Carlitz motives with Complex Multiplication, and establish an Ogus-type Chowla-Selberg formula. Furthermore, we prove the algebraic independence of these v-adic periods by employing the technique of switching "v and ∞", and determining the dimension of relevant motivic Galois groups on the "∞-adic" side through an adaptation and refinement of existing methods. As a consequence, all algebraic relations among v-adic arithmetic gamma values over \mathbbF_q(θ) can be derived from standard functional equations together with Thakur's analogue of the Gross-Koblitz formula.

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