Transcendental nature of \(p\)-adic digamma values (Q6631471)
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scientific article; zbMATH DE number 7937599
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Transcendental nature of \(p\)-adic digamma values |
scientific article; zbMATH DE number 7937599 |
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Transcendental nature of \(p\)-adic digamma values (English)
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1 November 2024
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The authors obtain generalizations of some earlier results by \textit{M. R. Murty} and \textit{N. Saradha} [Acta Arith. 133, No. 4, 349--362 (2008; Zbl 1253.11077)]; as well as \textit{T. Chatterjee} and \textit{S. Gun} [Acta Arith. 162, No. 2, 197--208 (2014; Zbl 1285.11105)] on the transcendental nature of certain \(p\)-adic digamma values. Particularly, they prove the transcendental nature of the \(p\)-adic digamma values corresponding to \(\psi_p(r/pq) + \gamma_p\), where \(p, q\) are distinct primes, and \(1\le r<pq/2\), and \((r,pq)=1\).
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digamma function
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Euler's constant
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\(p\)-adic analogue of Baker's theory
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\(p\)-adic analogue of classical functions
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primitive roots
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units in the cyclotomic fields
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