ArticleOriginal scientific text

Title

Short interval results for k-free values of irreducible polynomials

Authors 1

Affiliations

  1. Mathematics Department, University of South Carolina, Columbia, South Carolina 29208, U.S.A.

Bibliography

  1. M. Cugiani, Sugli intervalli fra i valori dell'argomento pei quali un polinomio risulta libero da potenze, Riv. Mat. Univ. Parma 4 (1953), 95-103.
  2. P. Erdős, Arithmetical properties of polynomials, J. London Math. Soc. 28 (1953), 416-425.
  3. M. Filaseta and O. Trifonov, On gaps between squarefree numbers, in: Analytic Number Theory, Proceedings of a Conference in Honor of Paul T. Bateman, Progr. Math. 85, B. C. Berndt, H. G. Diamond, H. Halberstam, and A. Hildebrand (eds.), Birkhäuser, Boston 1990, 235-253.
  4. M. Filaseta and O. Trifonov, On gaps between squarefree numbers II, J. London Math. Soc. (2) 45 (1992), 215-221.
  5. H. Halberstam and K. F. Roth, On the gaps between consecutive k-free integers, J. London Math. Soc. 26 (1951), 268-273.
  6. C. Hooley, On the power free values of polynomials, Mathematika 14 (1967), 21-26.
  7. M. N. Huxley and M. Nair, Power free values of polynomials III, Proc. London Math. Soc. 41 (1980), 66-82.
  8. T. Nagel, Zur Arithmetik der Polynome, Abh. Math. Sem. Hamburg. Univ. 1 (1922), 179-184.
  9. M. Nair, Power free values of polynomials, Mathematika 23 (1976), 159-183.
  10. M. Nair, Power free values of polynomials II, Proc. London Math. Soc. (3) 38 (1979), 353-368.
  11. G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Part VIII, prob. 86, p. 129), Springer, Berlin 1976.
  12. G. Ricci, Ricerche arithmetiche sui polinomi, Rend. Circ. Mat. Palermo 57 (1933), 433-475.
  13. O. Trifonov, On the squarefree problem, C. R. Acad. Bulgare Sci. 41 (12) (1988), 37-40.
  14. O. Trifonov, On the squarefree problem II, Math. Balkanica 3 (1989), 284-295.
  15. O. Trifonov, On gaps between k-free numbers, preprint.
Pages:
249-270
Main language of publication
English
Received
1992-09-28
Published
1993
Exact and natural sciences