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On q-analogue of Euler--Stieltjes constants.
- Source :
- Proceedings of the American Mathematical Society; May2023, Vol. 151 Issue 5, p2011-2022, 12p
- Publication Year :
- 2023
-
Abstract
- Kurokawa and Wakayama [Proc. Amer. Math. Soc. 132 (2004), pp. 935–943] defined a q-analogue of the Euler constant and proved the irrationality of certain numbers involving q-Euler constant. In this paper, we improve their results and prove the linear independence result involving q-analogue of the Euler constant. Further, we derive the closed-form of a q-analogue of the k-th Stieltjes constant \gamma _k(q). These constants are the coefficients in the Laurent series expansion of a q-analogue of the Riemann zeta function around s=1. Using a result of Nesterenko [C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), pp. 909–914], we also settle down a question of Erdős regarding the arithmetic nature of the infinite series \sum _{n\geq 1}{\sigma _1(n)}/{t^n} for any integer t > 1. Finally, we study the transcendence nature of some infinite series involving \gamma _1(2). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 151
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 162264436
- Full Text :
- https://doi.org/10.1090/proc/16288