Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T16:56:19.262Z Has data issue: false hasContentIssue false
  • English
  • Français

The values of a polynomial over a finite field

Published online by Cambridge University Press:  18 May 2009

S. D. Cohen
S. D. Cohen
Affiliation:
University of Glasgow, Glasgow G12 8QQ
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The object of this paper is to derive, using a version of the large sieve for function fields due to J. Johnsen [6], explicit lower boundsfor the average number of distinct values taken by a polynomial over a finite field.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 2 , September 1973 , pp. 205 - 208
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Birch, B. J. and Swinnerton-Dyer, H. P. F., Note on a problem of Chowla, Acta Arith. 5 (1959) 417–423.CrossRefGoogle Scholar
2.Carlitz, L., The arithmetic of polynomials in a Galois field, Amer. J. Math. 54 (1932), 39–50.CrossRefGoogle Scholar
3.Carlitz, L., On the number of distinct values of a polynomial with coefficients in a finite field, Proc. Japan. Acad. 31 (1955), 119–120.Google Scholar
4.Cohen, S. D., The distribution of polynomials over finite fields, Acta Arith. 17 (1970), 255–271.CrossRefGoogle Scholar
5.Cohen, S. D., Uniform distribution of polynomials over finite fields, J. London Math. Soc. (2) 6 (1972), 93–102.CrossRefGoogle Scholar
6.Johnsen, J., On the large sieve method in GF[q, x], Mathematika 18 (1971), 172–184.CrossRefGoogle Scholar
7.Uchiyama, S., Note on the mean value of V(f), Proc. Japan. Acad. 31 (1955), 199–201.Google Scholar
8.Uchiyama, S., Note on the mean value of V(f), II, Proc. Japan. Acad. 31 (1955), 321–323.Google Scholar