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Transcendental nature of p-adic digamma values.
- Source :
-
Research in Number Theory . 9/19/2024, Vol. 10 Issue 4, p1-19. 19p. - Publication Year :
- 2024
-
Abstract
- For a fixed prime p, Murty and Saradha (Acta Arith 133:349–362, 2008) studied the transcendental nature of special values of the p-adic digamma function, denoted as ψ p (r / p) + γ p . This research was later extended by Chatterjee and Gun in 2014, who investigated the case of ψ p (r / p n) + γ p , for any integer n > 1 . In this article, we generalize their results for distinct prime powers and explore the transcendental nature of the p-adic digamma values, with at most one exception. Further, we investigate the multiplicative independence of cyclotomic numbers satisfying certain conditions. Using this, we prove the transcendental nature of p-adic digamma values corresponding to ψ p (r / p q) + γ p , where p, q are distinct primes. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CYCLOTOMIC fields
*INTEGERS
*FIREARMS
Subjects
Details
- Language :
- English
- ISSN :
- 25220160
- Volume :
- 10
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Research in Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 179739638
- Full Text :
- https://doi.org/10.1007/s40993-024-00570-1