43 citations · 77 across the 11 of their papers we have counts for
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math.NT2002
A Hypergeometric Approach, Via Linear Forms Involving Logarithms, to Irrationality Criteria for Euler's Constant
Jonathan Sondow, Sergey Zlobin
Using an integral of a hypergeometric function, we give necessary and sufficient conditions for irrationality of Euler's constant . The proof is by reduction to known irrational…
math.NT2002
Criteria for Irrationality of Euler's Constant
Jonathan Sondow
By modifying Beukers' proof of Apery's theorem that zeta(3) is irrational, we derive criteria for irrationality of Euler's constant, gamma. For n > 0, we define a double integral I…
math.NT2002★ 2 cited
Zeros of the alternating zeta function on the line R(s)=1
Jonathan Sondow
The alternating zeta function zeta*(s) = 1 - 2^{-s} + 3^{-s} - ... is related to the Riemann zeta function by the identity (1-2^{1-s})zeta(s) = zeta*(s). We deduce the vanishing of…