Issue
RAIRO-Theor. Inf. Appl.
Volume 60, 2026
Diophantine Analysis and Related Topics (DART2025Z)
Article Number 25
Number of page(s) 11
DOI https://doi.org/10.1051/ita/2026024
Published online 31 July 2026
  1. I.I. Piatetski-Shapiro, On the distribution of prime numbers in the sequence of the form [f(n) J. Mat. Sb. 33 (1953) 559–566. [Google Scholar]
  2. Y. Akbal, Friable values of Piatetski-Shapiro sequences. Proc. Am. Math. Soc. 145 (2017) 4255–4268. [Google Scholar]
  3. Y. Akbal and A.M. Güloğlu, Waring-Goldbach problem with Piatetski-Shapiro primes. J. Theor. Nombres Bordeaux 30 (2018) 449–467. [Google Scholar]
  4. R.C. Baker and W.D. Banks, Character sums with Piatetski-Shapiro sequences. Q. J. Math. 66 (2015) 393–416. [Google Scholar]
  5. H. Li and H. Pan, Small gaps between the Piatetski-Shapiro primes. Trans. Am. Math. Soc. 373 (2020) 8463–8484. [Google Scholar]
  6. M. Filaseta, S.W. Graham and O. Trifonov, Starting with gaps between k-free numbers. Int. J. Number Theory 11 (2015) 1411–1435. [Google Scholar]
  7. F. Pappalardi, A Survey on k-freeness, Number Theory. Ramanujan Mathematical Society Lecture Notes Series, vol. 1. Ramanujan Mathematical Society, Mysore (2005) 71–88. [Google Scholar]
  8. I.E. Stux, Distribution of squarefree integers in non-linear sequences. Pacific J. Math. 59 (1975) 577–584. [Google Scholar]
  9. G.J. Rieger, Remark on a paper of Stux concerning squarefree numbers in non-linear sequences. Pacific J. Math. 78 (1978) 241–242. [Google Scholar]
  10. X. Cao and W. Zhai, The distribution of square-free numbers of the form [nc]. J. Theor. Nombres Bordeaux 10 (1998) 287–299. [Google Scholar]
  11. X. Cao and W. Zhai, Distribution of square-free numbers of the form [nc] (II). Acta Math. Sinica (Chinese Ser.) 51 (2008) 1187–1194 (in Chinese). [Google Scholar]
  12. M. Zhang and J. Li, Distribution of cube-free numbers with form [nc]. Front. Math. China 12 (2017) 1515–1525. [Google Scholar]
  13. J.M. Deshouillers, A remark on cube-free numbers in Segal-Piatetski-Shapiro sequences. Hardy-Ramanujan J. 41 (2018) 127–132. [Google Scholar]
  14. H.L. Montgomery, Ten lectures on the interface between analytic number theory and harmonic analysis, CBMS Regional Conference Series in Mathematics, vol. 84. Conf. Board Math. Sci., Washington, DC (1994); American Mathematical Society, Providence, RI (1994). [Google Scholar]
  15. S.W. Graham and G. Kolesnik, van der Corput's Method of Exponential Sums, LMS Lecture Note Series, vol. 126. Cambridge (1991). [Google Scholar]
  16. P. Sargos, Points entiers au voisinage d'une courbe, sommes trigonometriques courtes et paires d'exposants. Proc. London Math. Soc. 70 (1995) 285–312. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.