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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…