58
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

An Accurate Heuristic for a Problem of Shparlinski

References

  • [Apostol 76] T. M. Apostol. Introduction to Analytic Number Theory. New York-Heidelberg: Springer-Verlag, 1976.
  • [Dirichlet 37] P. G. L. Dirichlet. “Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält.” Abhand. Ak. Wiss. Berlin 48 (1837), 45–81.
  • [Ford et al. 05] K. Ford, M. R. Khan, I. Shparlinski, and C. L. Yankov. “On the Maximal Difference Between an Element and Its Inverse in Residue Rings.” Proc. Amer. Math. Soc. 133 (2005), 3463–3468.
  • [Granville 10] A. Granville. “Different Approaches to the Distribution of Primes.” Milan J. Math. 78 (2010), 64–85.
  • [Kahn 01] M. R. Kahn. “Problem 10736: an optimization with a modular constraint.” Amer. Math. Mon. 108 (2001), 374–375.
  • [Landau 00] E. Landau. “Ueber die zahlentheoretische Funktion ϕ(n) und ihre Beziehung zum Goldbachschen Satz.” Göttinger Nachr. (1900), Heft 2, 177–186.
  • [Landau 12] E. Landau. “Gelöste und ungelöste Probleme aus der Theorie der Primzahlverteilung und der Riemannschen Zetafunktion.” Jahresber. Deutsche Math. Ver. 21 (1912), 208–228.
  • [LeVeque 56] W. J. LeVeque. Topics in Number Theory (2 Volumes). Reading, MA: Addison-Wesley Publishing Co., Inc., 1956.
  • [Pintz 09] J. Pintz. “Landau’s Problems on Primes.” J. Théor. Nombres Bordeaux 21 (2009), 357–404.
  • [Ramaré and Rumely 96] O. Ramaré and R. Rumely. “Primes in arithmetic progressions.” Math. Comp. 65:213 (1996), 397–425.
  • [Shparlinski 12] I. Shparlinski. “Modular hyperbolas.” Jpn. J. Math. 7:2 (2012), 235–294.
  • [Walfisz 36] A. Walfisz. “Zur additiven Zahlentheorie. II.” Math. Z. 40:1 (1936), 592–607.

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.