Linear independence of q-analogue of the generalized Stieltjes constants over number fields

2024/04/11 by Tapas Chatterjee, Chatterjee, Tapas, Sonam Garg +1
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.09139

openalex publication_date 2024/04/11 · openalex created_date 2024/04/17 · openalex updated_date 2026/07/28

Abstract

In this article, we aim to extend the research conducted by Chatterjee and Garg in 2024, particularly focusing on the q-analogue of the generalized Stieltjes constants. These constants constitute the coefficients in the Laurent series expansion of a q-analogue of the Hurwitz zeta function around s=1. Chatterjee and Garg previously established arithmetic results related to γ₀(q,x), for q>1 and 0 < x <1 over the field of rational numbers. Here, we broaden their findings to encompass number fields \mathbbF in two scenarios: firstly, when \mathbbF is linearly disjoint from the cyclotomic field ℚ(ζ_b), and secondly, when \mathbbF has non-trivial intersection with ℚ(ζ_b), with b ≥ 3 being any positive integer.

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