Short interval results for k-free values of irreducible polynomials
Michael Filaseta
Acta Arithmetica, Tome 64 (1993), p. 249-270 / Harvested from The Polish Digital Mathematics Library
Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:206549
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     author = {Michael Filaseta},
     title = {Short interval results for k-free values of irreducible polynomials},
     journal = {Acta Arithmetica},
     volume = {64},
     year = {1993},
     pages = {249-270},
     zbl = {0782.11025},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav64i3p249bwm}
}
Michael Filaseta. Short interval results for k-free values of irreducible polynomials. Acta Arithmetica, Tome 64 (1993) pp. 249-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav64i3p249bwm/

[000] [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. | Zbl 0053.02603

[001] [2] P. Erdős, Arithmetical properties of polynomials, J. London Math. Soc. 28 (1953), 416-425. | Zbl 0051.27703

[002] [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. | Zbl 0723.11044

[003] [4] M. Filaseta and O. Trifonov, On gaps between squarefree numbers II, J. London Math. Soc. (2) 45 (1992), 215-221.

[004] [5] H. Halberstam and K. F. Roth, On the gaps between consecutive k-free integers, J. London Math. Soc. 26 (1951), 268-273. | Zbl 0043.04901

[005] [6] C. Hooley, On the power free values of polynomials, Mathematika 14 (1967), 21-26. | Zbl 0166.05203

[006] [7] M. N. Huxley and M. Nair, Power free values of polynomials III, Proc. London Math. Soc. 41 (1980), 66-82. | Zbl 0435.10026

[007] [8] T. Nagel, Zur Arithmetik der Polynome, Abh. Math. Sem. Hamburg. Univ. 1 (1922), 179-184. | Zbl 48.0132.04

[008] [9] M. Nair, Power free values of polynomials, Mathematika 23 (1976), 159-183. | Zbl 0349.10039

[009] [10] M. Nair, Power free values of polynomials II, Proc. London Math. Soc. (3) 38 (1979), 353-368. | Zbl 0404.10020

[010] [11] G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Part VIII, prob. 86, p. 129), Springer, Berlin 1976.

[011] [12] G. Ricci, Ricerche arithmetiche sui polinomi, Rend. Circ. Mat. Palermo 57 (1933), 433-475. | Zbl 59.0214.02

[012] [13] O. Trifonov, On the squarefree problem, C. R. Acad. Bulgare Sci. 41 (12) (1988), 37-40. | Zbl 0669.10065

[013] [14] O. Trifonov, On the squarefree problem II, Math. Balkanica 3 (1989), 284-295. | Zbl 0698.10028

[014] [15] O. Trifonov, On gaps between k-free numbers, preprint. | Zbl 0841.11046