Gun, Sanoli ; Murty, M. Ram ; Rath, Purusottam (2009) Transcendence of the log gamma function and some discrete periods Journal of Number Theory, 129 (9). pp. 2154-2165. ISSN 0022-314X
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Official URL: http://doi.org/10.1016/j.jnt.2009.01.008
Related URL: http://dx.doi.org/10.1016/j.jnt.2009.01.008
Abstract
We study transcendental values of the logarithm of the gamma function. For instance, we show that for any rational number x with 0<x<1, the number logΓ(x)+logΓ(1-x) is transcendental with at most one possible exception. Assuming Schanuel's conjecture, this possible exception can be ruled out. Further, we derive a variety of results on the Γ-function as well as the transcendence of certain series of the form Σ∞ n1P(n)/Q(n), where P(x) and Q(x) are polynomials with algebraic coefficients.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier B.V. |
| Keywords: | Gamma Function; Log Gamma Function; Schanuel's Conjecture; Periods. |
| ID Code: | 117991 |
| Deposited On: | 10 May 2021 12:55 |
| Last Modified: | 10 May 2021 12:55 |
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