Skip to main content
Log in

Exponential sums and prime divisors of sparse integers

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We obtain a new lower bound on the number of prime divisors of integers whose g-ary expansion contains a fixed number of nonzero digits.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W. D. Banks, M. Z. Garaev, F. Luca and I. E. Shparlinski, Uniform distribution of fractional parts related to pseudoprimes, Canad. J. Math., to appear.

  2. W. D. Banks and I. E. Shparlinski, Arithmetic properties of numbers with restricted digits, Acta Arith., 112 (2004), 313–332.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Bourgain, Estimates on exponential sums related to Diffie-Hellman distributions, Geom. Funct. Anal., 15 (2005), 1–34.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Erdős and R. Murty, On the order of a (mod p), Proc. 5th Canadian Number Theory Association Conf., Amer. Math. Soc., Providence, RI, 1999, 87–97.

    Google Scholar 

  5. E. Fouvry and C. Mauduit, Methódes des crible et fonctions sommes des chiffres, Acta Arith., 77 (1996), 339–351.

    MATH  MathSciNet  Google Scholar 

  6. E. Fouvry and C. Mauduit, Sommes des chiffres et nombres presque premiers, Math. Ann., 305 (1996), 571–599.

    Article  MATH  MathSciNet  Google Scholar 

  7. K.-H. Indlekofer and N. M. Timofeev, Divisors of shifted primes, Publ. Math. Debrecen, 60 (2002), 307–345.

    MATH  MathSciNet  Google Scholar 

  8. S. Konyagin, Arithmetic properties of integers with missing digits: distribution in residue classes, Period. Math. Hungar., 42 (2001), 145–162.

    Article  MATH  MathSciNet  Google Scholar 

  9. S. V. Konyagin, C. Mauduit and A. Sárkőzy, On the number of prime factors of integers characterized by digit properties, Period. Math. Hungar., 40 (2000), 37–52.

    Article  MATH  MathSciNet  Google Scholar 

  10. F. Luca, Arithmetic properties of positive integers with fixed digit sum, preprint, 2002.

  11. C. Mauduit and A. Sárközy, On the arithmetic structure of sets characterized by sum of digits properties, J. Number Theory, 61 (1996), 25–38.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Mauduit and A. Sárközy, On the arithmetic structure of the integers whose sum of digits is fixed, Acta Arith., 81 (1997), 145–173.

    MATH  MathSciNet  Google Scholar 

  13. F. Pappalardi, On the order of finitely generated subgroups of Q* (mod p) and divisors of p − 1, J. Number Theory, 57 (1996), 207–222.

    Article  MATH  MathSciNet  Google Scholar 

  14. I. E. Shparlinski, Prime divisors of sparse integers, Period. Math. Hungar., 46 (2003), 215–222.

    Article  MATH  MathSciNet  Google Scholar 

  15. C. L. Stewart, On the representation of an integer in two different bases, J. Reine Angew. Math., 319 (1980), 63–72.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Igor E. Shparlinski.

Additional information

Communicated by Attila Pethő

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shparlinski, I.E. Exponential sums and prime divisors of sparse integers. Period Math Hung 57, 93–99 (2008). https://doi.org/10.1007/s10998-008-7093-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-008-7093-3

Mathematics subject classification numbers

Key words and phrases

Navigation