OFFSET
0,1
COMMENTS
This number arose in the Davenport-Heilbronn zeta-function which satisfies a functional equation (like zeta) but does not satisfy RH. Some nontrivial zeros are off the critical line (see reference).
REFERENCES
P. Borwein et al., The Riemann Hypothesis, Springer (2009), 136-137.
LINKS
E. Bombieri and D. Hejhal, Sur les zéros des fonctions zeta d'Epstein, (mostly in English) Comptes rendus de l'Académie des Sciences, Paris, 304 (1987), 213-217.
H. Davenport and H. Heilbronn, On the zeros of certain Dirichlet series I, J. London Math. Soc. 11 (1936), 181-185.
H. Davenport and H. Heilbronn, On the zeros of certain Dirichlet series II, J. London Math. Soc. 11 (1936), 307-312.
EXAMPLE
0.27678717...
MATHEMATICA
RealDigits[ArcTan[(Sqrt[10-2*Sqrt[5]]-2)/(Sqrt[5]-1)], 10, 120][[1]] (* Harvey P. Dale, Mar 03 2018 *)
PROG
(PARI) atan((sqrt(10-2*sqrt(5))-2)/(sqrt(5)-1)) \\ Charles R Greathouse IV, Mar 10 2016
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, Mar 14 2009
EXTENSIONS
Keyword:cons inserted, leading zero and offset adjusted by R. J. Mathar, Jul 15 2010
STATUS
approved