C. Cobeli, A. Zaharescu — The Haros-Farey Sequence at Two Hundred Years
[Cru2000] W. da Cruz, Fractons and fractal statistics, Internat. J. Modern Phys. A 15 2000, no. 24,
3805–3828. [Cru2001]
W. da Cruz Fractal statistics, fractal index and fractons, Geometrical aspects of quantum fields Londrina, 2000, 73–79, World Sci. Publishing, River Edge, NJ, 2001.
[CO2000] W. da Cruz and R. de Oliveira, Fractal index, central charge and fractons, Modern Phys.
Lett. A 15 2000, no. 31, 1931–1939.
[Cvi1992] P. Cvitanovi´c, Circle maps: irrationally winding, From Number Theory to Physics Les
Houches, 1989, 631–658, Springer, Berlin, 1992. [Del1974]
H. Delange, Sur les suites de Farey, Journ´ees Arithm´etiques Grenoble, 1973, pp. 39–47. Bull. Soc. Math. France Mem., No. 37, Soc. Math. France, Paris, 1974.
[DD1993] F. Delmer and J. M. Deshouillers, On a generalization of Farey sequences I, Contemp. Math.,
143, Amer. Math. Soc., Providence, RI, 1993, 243–246. [DD1995]
F. Delmer and J. M. Deshouillers, On a generalization of Farey sequences II, J. Number Theory 55 1995, no. 1, 60–67.
[Dic1938] L. E. Dickson, History of the Theory of Numbers, Clarendon Press , Oxford University Press,
1938. [Dre1999]
F. Dress, Discr´epance des suites de Farey, J. Th´eor. Nombres Bordeaux 11 1999, no. 2, 345–367.
[DFI1994] W. Duke, J. Friedlander and H. Iwaniek, A quadratic divisor problem, Invent. Math. 115
1994, 209–217. [Far1816e]
J. Farey, On a curious property of vulgar fractions, Philos. Mag. J. 47 1816, 385–386.
[Far1816f] J. Farey, Propri´et´e curieuse des fractions ordinaires, Bull. Sc. Soc. Philomatique 3 1816,
no. 3, 112. [For1938]
L. R. Ford, Fractions, A.M.S. 45 1938, no. 9, 586–601.
[Fra1924] J. Franel, Les suites de Farey et les probl`emes des nombres premiers, Nachr. Ges. Wiss.
G¨ottingen Math.-Phys. Kl. 1924, 198–201. [Gol2000]
R. N. Gologan, Snooker and Farey fractions, preprint 2000. [Har1959]
G. H. Hardy, A mathematician’s apology, Englewood Cliffs, Prentice-Hall, 1959. [HW1979]
G. H. Hardy and E. M. Wright, An introduction to the Theory of Numbers, Fifth edition, The Clarendon Press, Oxford University Press, New York, 1979. xvi+426 pp.
[Hal1970] R. R. Hall, A note on Farey series, J. London Math. Soc. 2 1970, no. 2, 139–148.
[Hal1994] R. R. Hall, On consecutice Farey arcs II, Acta Arith., 66 1994, no. 1, 1–9.
[HS2001] R. R. Hall and P. Shiu, The index of a Farey sequence, preprint 2001.
[HT1984] R. R. Hall and G. Tanenbaum, On consecutice Farey arcs, Acta Arith., 44 1984, 397–405.
[Har1802] C. Haros, Tables pour ´evaluer une fraction ordinaire avec autand de decimals qu’on voudra;
et pour trover la fraction ordinaire la plus simple, et qui a approche sensiblement d’une fraction d´ecimale
, J. Ecole Polytechn. 4 1802, 364–368.
[Hay2001] A. Haynes, A note on Farey fractions with odd denominators, to appear in J. Number Theory.
[Hur1894] A. Hurwitz, ¨
Uber die angen¨aherte Darstellung der Zahlen durch rationale Br¨uche , Math.
Ann. 44 1894, 417–436.
[Hux1971] M. N. Huxley, The distribution of Farey points. I., Acta Arith. 18 1971, 281–287.
[Kan1978] S. Kanemitsu, On some sums involving Farey fractions, Math. J. Okayama Univ. 20 1978,
no. 2, 101–113. [Kan1980]
S. Kanemitsu, Corrigenda to: ”On some sums involving Farey fractions”, Math. J. Okayama Univ. 22 1980, no. 2, 223–224.
C. Cobeli, A. Zaharescu — The Haros-Farey Sequence at Two Hundred Years
[KKY2000] S. Kanemitsu, T. Kuzumaki and M. Yoshimoto, Some sums involving Farey fractions II, J.
Math. Soc. Japan 52 2000, no. 4, 915–947.
[KRS1982] S. Kanemitsu, R. Sita Rama Chandra Rao and A. Siva Rama Sarma, Some sums involving
Farey fractions I
, J. Math. Soc. Japan, 34 1982, 125–142.
[KY1996] S. Kanemitsu and M. Yoshimoto, Farey series and the Riemann hypothesis, Acta Arith. 75
1996, no. 4, 351–375. [KY1997]
S. Kanemitsu and M. Yoshimoto, Farey series and the Riemann hypothesis III, International Symposium on Number Theory Madras, 1996. Ramanujan J. 1 1997, no. 4, 363–368.
[KZ1996] P. Kargaev and A. Zhigljavsky, Approximations of real numbers by rationals: some metric
theorems
, J. Number Theory, 61 1996, no. 2, 209–225.
[KZ1997] P. Kargaev and A. Zhigljavsky, Asymptotic distribution of the distance function to the Farey
points
, J. Number Theory, 65 1997, no. 1, 130–149.
[Kho2001] A. L. Kholodenko, Statistical mechanics of
ç➂è①â
gravity from Riemann zeta function and Alexander polynomial: exact results
, J. Geom. Phys. 38 2001, no. 2, 81–139.
[KO] P. Kleban and A. E. ¨
Ozl¨uk, A Farey fraction spin chain, Comm. Math. Phys. 203 1999, no.
3, 635–647. [Kna1993]
A. Knauf, On a ferromagnetic spin chain, Comm. Math. Phys. 153 1993, 77–115.
