On p -adic Euler constants

Abhishek Bharadwaj

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 283-308
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Bharadwaj, Abhishek. "On $p$-adic Euler constants." Czechoslovak Mathematical Journal (2021): 283-308. <http://eudml.org/doc/297111>.

@article{Bharadwaj2021,
abstract = {The goal of this article is to associate a $p$-adic analytic function to the Euler constants $\gamma _p (a, F)$, study the properties of these functions in the neighborhood of $s=1$ and introduce a $p$-adic analogue of the infinite sum $\sum _\{n \ge 1\} f(n) / n$ 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.},
author = {Bharadwaj, Abhishek},
journal = {Czechoslovak Mathematical Journal},
keywords = {$p$-adic Euler-Lehmer constant; linear forms in logarithms},
language = {eng},
number = {1},
pages = {283-308},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $p$-adic Euler constants},
url = {http://eudml.org/doc/297111},
year = {2021},
}

TY - JOUR
AU - Bharadwaj, Abhishek
TI - On $p$-adic Euler constants
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 283
EP - 308
AB - The goal of this article is to associate a $p$-adic analytic function to the Euler constants $\gamma _p (a, F)$, study the properties of these functions in the neighborhood of $s=1$ and introduce a $p$-adic analogue of the infinite sum $\sum _{n \ge 1} f(n) / n$ 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.
LA - eng
KW - $p$-adic Euler-Lehmer constant; linear forms in logarithms
UR - http://eudml.org/doc/297111
ER -

References

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