OFFSET
1,1
COMMENTS
Imaginary part of the first complex zero of the alternating zeta function. The pair a=1, b=2*Pi/log(2) is a counterexample to the incorrect reformulation of the Riemann Hypothesis in J. Havil's book Gamma: Exploring Euler's Constant. See Sondow (2012).
Also the Bekenstein bound in natural (Planck) units: the information (in bits) contained in a system with mass m and radius r is at most this constant times m*r. - Charles R Greathouse IV, Aug 19 2015
REFERENCES
J. Havil, Gamma: Exploring Euler's Constant, Princeton Univ. Press, 2003, p. 207.
LINKS
J. Sondow, Zeros of the alternating zeta function on the line R(s)=1, arXiv:math/0209393 [math.NT], 2002-2003.
J. Sondow, Zeros of the alternating zeta function on the line R(s)=1, Amer. Math. Monthly 110 (2003) 435-437.
J. Sondow, A Simple Counterexample to Havil's "Reformulation" of the Riemann Hypothesis, arXiv:0706.2840 [math.NT], 2007-2010.
J. Sondow, A Simple Counterexample to Havil's "Reformulation" of the Riemann Hypothesis, Elemente der Mathematik 67 (2012), pp. 61-67.
EXAMPLE
9.0647202836543...
MATHEMATICA
RealDigits[ N[ 2*Pi/Log[2], 105]] [[1]]
PROG
(PARI) 2*Pi/log(2) \\ Charles R Greathouse IV, Aug 19 2015
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jonathan Sondow, Jun 19 2007
STATUS
approved