On certain solutions of the diophantine equation x-y = p(z)

• Autorzy: R. Nair
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1992
• Tom: 62
• Numer: 1
• Strony: 61-71

Daty

wydano

1992

otrzymano

1991-08-16

poprawiono

1992-01-31

Twórcy

autor

R. Nair

• Department of Pure Mathematics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, U.K.

Bibliografia

• [1] V. Bergelson, Sets of recurrence of $ℤ^m$-actionsand properties of sets of differences in $ℤ^m$, J. London Math. Soc. (2) 31 (1985), 295-304.
• [2] A. Bertrand-Mathis, Ensembles intersectifs et recurrence de Poincaré, Israel J. Math. 55 (1986), 184-198.
• [3] H. Furstenberg, Ergodic behaviour of diagonal measures and a theorem of Szemerédi onarithmetic progressions, J. Analyse Math. 31 (1977), 204-256.
• [4] H. Furstenberg, Recurrence in Ergodic Theory andCombinatorial Number Theory, Princeton University Press, 1981.
• [5] L. K. Hua, Additive Theory of Prime Numbers, Amer. Math. Soc.Transl. 13, 1965.
• [6] T. Kamae and M. Mendès France, Van der Corput's difference theorem, Israel J. Math. 31 (1978),335-342.
• [7] U. Krengel, Ergodic Theorems, de Gruyter Stud. Math. 6, 1985.
• [8] R. Nair, On strong uniform distribution, Acta Arith. 56 (1990), 183-193.
• [9] G. Rhin, Sur la répartition modulo 1 des suites f(p), Acta Arith. 23 (1973), 217-248.
• [10] A. Sárközy, On difference sets of sequences of integers, II, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 21(1978), 45-53.
• [11] A. Sárközy, On difference sets of sequences ofintegers. III, Acta Math. Acad. Sci. Hungar. 31 (3-4) (1978),355-386.
• [12] H. Weyl, Über die Gleichverteilung von Zahlenmod. Eins, Math. Ann. 77 (1916), 313-352.