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International Journal of Mathematics and Mathematical Sciences
Volume 2007, Article ID 37853, 5 pages
http://dx.doi.org/10.1155/2007/37853
Research Article

Distribution of Roots of Polynomial Congruences

Department of Computing, Macquarie University, Sydney 2109, NSW, Australia

Received 7 March 2007; Accepted 7 June 2007

Academic Editor: George E. Andrews

Copyright © 2007 Igor E. Shparlinski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Hooley, “On the distribution of the roots of polynomial congruences,” Mathematika, vol. 11, pp. 39–49, 1964. View at Zentralblatt MATH · View at MathSciNet
  2. C. Hooley, “On the greatest prime factor of a quadratic polynomial,” Acta Mathematica, vol. 117, no. 1, pp. 281–299, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. Duke, J. B. Friedlander, and H. Iwaniec, “Equidistribution of roots of a quadratic congruence to prime moduli,” Annals of Mathematics, vol. 141, no. 2, pp. 423–441, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Á. Tóth, “Roots of quadratic congruences,” International Mathematics Research Notices, vol. 2000, no. 14, pp. 719–739, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  5. H. Weyl, “Zur Abschätzung von ζ(1+it),” Annals of Mathematics, vol. 10, pp. 88–101, 1921.
  6. H. Iwaniec and E. Kowalski, Analytic Number Theory, vol. 53 of American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, RI, USA, 2004. View at Zentralblatt MATH · View at MathSciNet
  7. B. Poonen and J. F. Voloch, “Random Diophantine equations,” in Arithmetic of Higher-Dimensional Algebraic Varieties (Palo Alto, Calif, 2002), vol. 226 of Progr. Math., pp. 175–184, Birkhäuser, Boston, Mass, USA, 2004. View at MathSciNet
  8. E. Bombieri, “On exponential sums in finite fields,” American Journal of Mathematics, vol. 88, no. 1, pp. 71–105, 1966. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Granville, I. E. Shparlinski, and A. Zaharescu, “On the distribution of rational functions along a curve over Fp and residue races,” Journal of Number Theory, vol. 112, no. 2, pp. 216–237, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet