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

R. Nair

Acta Arithmetica (1992)

  • Volume: 62, Issue: 1, page 61-71
  • ISSN: 0065-1036

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R. Nair. "On certain solutions of the diophantine equation x-y = p(z)." Acta Arithmetica 62.1 (1992): 61-71. <http://eudml.org/doc/206480>.

@article{R1992,
author = {R. Nair},
journal = {Acta Arithmetica},
keywords = {sets of recurrence; intersective subsets; difference sets; polynomial with integer coefficients; positive Banach density; ergodic theory; uniform distribution of polynomial values},
language = {eng},
number = {1},
pages = {61-71},
title = {On certain solutions of the diophantine equation x-y = p(z)},
url = {http://eudml.org/doc/206480},
volume = {62},
year = {1992},
}

TY - JOUR
AU - R. Nair
TI - On certain solutions of the diophantine equation x-y = p(z)
JO - Acta Arithmetica
PY - 1992
VL - 62
IS - 1
SP - 61
EP - 71
LA - eng
KW - sets of recurrence; intersective subsets; difference sets; polynomial with integer coefficients; positive Banach density; ergodic theory; uniform distribution of polynomial values
UR - http://eudml.org/doc/206480
ER -

References

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  1. [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. Zbl0579.10029
  2. [2] A. Bertrand-Mathis, Ensembles intersectifs et recurrence de Poincaré, Israel J. Math. 55 (1986), 184-198. Zbl0611.10032
  3. [3] H. Furstenberg, Ergodic behaviour of diagonal measures and a theorem of Szemerédi onarithmetic progressions, J. Analyse Math. 31 (1977), 204-256. Zbl0347.28016
  4. [4] H. Furstenberg, Recurrence in Ergodic Theory andCombinatorial Number Theory, Princeton University Press, 1981. 
  5. [5] L. K. Hua, Additive Theory of Prime Numbers, Amer. Math. Soc.Transl. 13, 1965. Zbl0192.39304
  6. [6] T. Kamae and M. Mendès France, Van der Corput's difference theorem, Israel J. Math. 31 (1978),335-342. Zbl0396.10040
  7. [7] U. Krengel, Ergodic Theorems, de Gruyter Stud. Math. 6, 1985. 
  8. [8] R. Nair, On strong uniform distribution, Acta Arith. 56 (1990), 183-193. Zbl0716.11036
  9. [9] G. Rhin, Sur la répartition modulo 1 des suites f(p), Acta Arith. 23 (1973), 217-248. 
  10. [10] A. Sárközy, On difference sets of sequences of integers, II, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 21(1978), 45-53. Zbl0413.10051
  11. [11] A. Sárközy, On difference sets of sequences ofintegers. III, Acta Math. Acad. Sci. Hungar. 31 (3-4) (1978),355-386. 
  12. [12] H. Weyl, Über die Gleichverteilung von Zahlenmod. Eins, Math. Ann. 77 (1916), 313-352. Zbl46.0278.06

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