Transcendental values of the digamma function

@inproceedings{Murty2007TranscendentalVO,
  title={Transcendental values of the digamma function},
  author={M. Ram Murty and N. Saradha},
  year={2007}
}
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, is algebraic. © 2007 Elsevier Inc. All rights reserved. MSC: primary 11J81; secondary 11J86, 11J91 
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