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Transcendental values of the digamma function

✍ Scribed by M. Ram Murty; N. Saradha

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 168 KB
Volume: 125
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.09.017

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✦ Synopsis

Let ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler's -function. Let q be a positive integer greater than 1 and γ denote Euler's constant. We show that all the numbers ψ(a/q) + γ, (a, q) = 1, 1 a q, are transcendental. We also prove that at most one of the numbers γ, ψ(a/q), (a, q) = 1, 1 a q,

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