Transcendental values of the digamma fun
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M. Ram Murty; N. Saradha
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Article
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2007
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Elsevier Science
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English
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Let ฯ(x) denote the digamma function, that is, the logarithmic derivative of Euler's -function. Let q be a positive integer greater than 1 and ฮณ denote Euler's constant. We show that all the numbers ฯ(a/q) + ฮณ, (a, q) = 1, 1 a q, are transcendental. We also prove that at most one of the numbers ฮณ, ฯ