| Title:
|
On $p$-adic Euler constants (English) |
| Author:
|
Bharadwaj, Abhishek |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
283-308 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$p$-adic Euler-Lehmer constant |
| Keyword:
|
linear forms in logarithms |
| MSC:
|
11J91 |
| idZBL:
|
07332717 |
| idMR:
|
MR4226482 |
| DOI:
|
10.21136/CMJ.2020.0336-19 |
| . |
| Date available:
|
2021-03-12T16:15:40Z |
| Last updated:
|
2023-04-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148740 |
| . |
| Reference:
|
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