93
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On Toric Orbits in the Affine Sieve

ORCID Icon & ORCID Icon

References

  • [Bourgain et al. 10] J. Bourgain, A. Gamburd, and P. Sarnak. “Affine Linear Sieve, Expanders, and Sum-product.” Invent. Math. 179:3 (2010), 559–644.
  • [Bober et al. 09] J. Bober, J. Lagarias, and B. Schmuland. “Very Composite Numbers: 11334 [2008, 71].” The American Mathematical Monthly. 116:9 (2009), 847–848.
  • [Bugeaud et al. 05] Y. Bugeaud, F. Luca, M. Mignotte, and S. Siksek. “On Fibonacci Numbers with Few Prime Divisors.” Proc. Japan Acad. Ser. A Math. Sci. 81:2 (2005), 17–20.
  • [Cassels 78] J. W. S. Cassels. Rational Quadratic Forms. Number 13 in London Mathematical Society Monographs. London: Academic Press, 1978.
  • [Hardy and Ramanujan 17] G. H. Hardy, and S. Ramanujan. “The Normal Number of Prime Factors of a Number n, Quart.” J. Pure Appl. Math. 48 (1917), 76–97.
  • [Kontorovich 14] A. Kontorovich. “Levels of Distribution and the Affine Sieve.” Ann. Fac. Sci. Toulouse Math. 23:5 (2014), 933–966.
  • [Kontorovich 16] A. Kontorovich. “Applications of thin orbits.” In Dynamics and Analytic Number Theory, Volume 437 of London Math. Soc. Lecture Note Ser. pages 289–317 Cambridge: Cambridge University Press, 2016.
  • [Lenstra and Pomerance 11] H. W. Lenstra, Jr., and C. Pomerance. “Primality Testing with Gaussian Periods.” J. European Math. Society. to appear. http://www.math.dartmouth.edu/∼carlp/aks041411.pdf.
  • [Mer] http://mersennus.net/fibonacci/. Contact: [email protected]
  • [Nicolas 84] J.-L. Nicolas. “Sur la distribution des nombres entiers ayant une quantité fixée de facteurs premiers.” Acta Arith. 44:3 (1984), 191–200.
  • [OEI a] Online Encyclopedia of Integer Sequences (OEIS), published electronically at https://oeis.org, 2019, Sequence A001605. https://oeis.org/A001605.
  • [OEI b] Online Encyclopedia of Integer Sequences (OEIS), published electronically at https://oeis.org, 2019, Sequence A001606. https://oeis.org/A001606.
  • [Salehi Golsefidy and Sarnak 13] A. Salehi Golsefidy, and P. Sarnak. “The Affine Sieve.” J. Amer. Math. Soc. 26:4 (2013), 1085–1105.
  • [Selberg 54] A. Selberg. “Note on a paper by L. G. Sathe.” J. Indian Math. Soc. 18 (1954), 53–57. [Also in: A. Selberg, Collected Papers, Vol. 1, Berlin: Springer-Verlag, 1989, pp. 418–422.]
  • [Tenenbaum 95] G. Tenenbaum. Introduction to Analytic and Probabilistic Number Theory, Volume 46 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 1995. translated from the second french edition (1995) by C. B. Thomas.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.