On p-ADIC Euler Constants

The goal of this article is to associate a p -adic analytic function to the Euler constants γ p ( a, F ), study the properties of these functions in the neighborhood of s = 1 and introduce a p -adic analogue of the infinite sum ∑ n ⩾ 1 f ( n ) / n # for an algebraic valued, periodic function f . Aft...

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Bibliographic Details
Published inCzechoslovak mathematical journal Vol. 71; no. 1; pp. 283 - 308
Main Author Bharadwaj, Abhishek
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2021
Springer Nature B.V
Subjects
Analysis
Analytic functions
Constants
Convex and Discrete Geometry
Irrationality
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Periodic functions
adic Euler-Lehmer constant
linear forms in logarithms
11J91
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Summary:The goal of this article is to associate a p -adic analytic function to the Euler constants γ p ( a, F ), study the properties of these functions in the neighborhood of s = 1 and introduce a p -adic analogue of the infinite sum ∑ n ⩾ 1 f ( n ) / n # for an algebraic valued, periodic function f . After this, we prove the theorem of Baker, Birch and Wirsing in this setup and discuss irrationality results associated to p -adic Euler constants generalising the earlier known results in this direction. Finally, we define and prove certain properties of p -adic Euler-Briggs constants analogous to the ones proved by Gun, Saha and Sinha.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2020.0336-19