The h-spacing distribution between Farey points

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 131, Issue 1, 2001, Pages 23-38

  Augustin, Volker ^a   Boca, Florin P ^b,c   Cobeli, Cristian ^c   Zaharescu, Alexandru ^c,d  

^a Cardiff University ^*  (Germany)

^b CARDIFF UNIVERSITY   (United Kingdom)

^c INSTITUTE OF MATHEMATICS   (Romania)

^d INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044527668     PISSN: 03050041     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0305004101005187     Document Type: Article

References (13)

1. F. P. BOCA, C. COBELI and A. ZAHARESCU. Distribution of lattice points visible from the origin. Commun. Math. Phys. 213 (2000), 433-470.
2. F. P. BOCA, C. COBELI and A. ZAHARESCU. A conjecture of R. R. Hall on Farey arcs, to appear in J. Reine Angew. Mathematik.
3. J. FRANEL. Les suites de Farey et le problème, des nombres premiers (Gottinger Nachr., 1924), pp. 198-201.
4. E. LANDAU. Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel (Gottinger Nachr., 1924), pp. 202-206.
5. R. R. HALL. A note on Farey series. J. London Math. Soc. 2 (1970), 139-148.
6. R. R. HALL. On consecutive Farey arcs II. Acta Arith. 66 (1994), 1-9.
7. R. R. HALL and G. TENENBAUM. On consecutive Farey arcs. Acta Arith. 44 (1984), 397-405.
8. R. R. HALL and G. TENENBAUM. The set of multiples of a short interval in Number theory, New York Seminar 1989-1990, D. V. Chudnovsky, G. V. Chudnovsky, H. Cohn and M. B. Nathanson (eds.) (Springer, 1991), pp. 119-128.
9. G. H. HARDY and E. M. WRIGHT. An introduction to the theory of numbers (Clarendon Press, 1938) (4th edition 1960).
10. M. HUXLEY. The distribution of Farey points I. Acta Arith. 18 (1971), 281-287.
11. 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.
12. P. KARGAEV and A. ZHIGLJAVSKY. Approximation of real numbers by rationals: some metric theorems. J. Number Theory 61 (1996), 209-225.
13. P. KARGAEV and A. ZHIGLJAVSKY. Asymptotic distribution of the distance function to the Farey points. J. Number Theory 65 (1997), 130-149.