13 citations · 26 across the 5 of their papers we have counts for
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Irrationality Measures, Irrationality Bases, and a Theorem of Jarnik
Jonathan Sondow
In math.NT/0307308 we defined the irrationality base of an irrational number and, assuming a stronger hypothesis than the irrationality of Euler's constant, gave a conditional uppe…
An irrationality measure for Liouville numbers and conditional measures for Euler's constant
Jonathan Sondow
The irrationality exponent of an irrational number t, defined using the irrationality measure , distinguishes among non-Liouville numbers and is infinite for Liouvill…
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…
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…