Transcendence of the log gamma function and some discrete periods |
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Authors: | Sanoli Gun M. Ram Murty Purusottam Rath |
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Affiliation: | Department of Mathematics and Statistics, Queen's University, Jeffrey Hall, 99 University Avenue, Kingston, ON, Canada K7L 3N6 |
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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 , where P(x) and Q(x) are polynomials with algebraic coefficients. |
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Keywords: | 11J81 11J86 11J91 |
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