Short interval results for k-free values of irreducible polynomials

Michael Filaseta

Acta Arithmetica (1993)

  • Volume: 64, Issue: 3, page 249-270
  • ISSN: 0065-1036

How to cite

top

Michael Filaseta. "Short interval results for k-free values of irreducible polynomials." Acta Arithmetica 64.3 (1993): 249-270. <http://eudml.org/doc/206549>.

@article{MichaelFilaseta1993,
author = {Michael Filaseta},
journal = {Acta Arithmetica},
keywords = {-free values of irreducible polynomials; short intervals; power-free values of polynomials; method of divided differences},
language = {eng},
number = {3},
pages = {249-270},
title = {Short interval results for k-free values of irreducible polynomials},
url = {http://eudml.org/doc/206549},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Michael Filaseta
TI - Short interval results for k-free values of irreducible polynomials
JO - Acta Arithmetica
PY - 1993
VL - 64
IS - 3
SP - 249
EP - 270
LA - eng
KW - -free values of irreducible polynomials; short intervals; power-free values of polynomials; method of divided differences
UR - http://eudml.org/doc/206549
ER -

References

top
  1. [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. Zbl0053.02603
  2. [2] P. Erdős, Arithmetical properties of polynomials, J. London Math. Soc. 28 (1953), 416-425. Zbl0051.27703
  3. [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. Zbl0723.11044
  4. [4] M. Filaseta and O. Trifonov, On gaps between squarefree numbers II, J. London Math. Soc. (2) 45 (1992), 215-221. 
  5. [5] H. Halberstam and K. F. Roth, On the gaps between consecutive k-free integers, J. London Math. Soc. 26 (1951), 268-273. Zbl0043.04901
  6. [6] C. Hooley, On the power free values of polynomials, Mathematika 14 (1967), 21-26. Zbl0166.05203
  7. [7] M. N. Huxley and M. Nair, Power free values of polynomials III, Proc. London Math. Soc. 41 (1980), 66-82. Zbl0435.10026
  8. [8] T. Nagel, Zur Arithmetik der Polynome, Abh. Math. Sem. Hamburg. Univ. 1 (1922), 179-184. Zbl48.0132.04
  9. [9] M. Nair, Power free values of polynomials, Mathematika 23 (1976), 159-183. Zbl0349.10039
  10. [10] M. Nair, Power free values of polynomials II, Proc. London Math. Soc. (3) 38 (1979), 353-368. Zbl0404.10020
  11. [11] G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Part VIII, prob. 86, p. 129), Springer, Berlin 1976. 
  12. [12] G. Ricci, Ricerche arithmetiche sui polinomi, Rend. Circ. Mat. Palermo 57 (1933), 433-475. Zbl59.0214.02
  13. [13] O. Trifonov, On the squarefree problem, C. R. Acad. Bulgare Sci. 41 (12) (1988), 37-40. Zbl0669.10065
  14. [14] O. Trifonov, On the squarefree problem II, Math. Balkanica 3 (1989), 284-295. Zbl0698.10028
  15. [15] O. Trifonov, On gaps between k-free numbers, preprint. Zbl0841.11046

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.