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Polynomials over finite fields with minimal value sets

Published online by Cambridge University Press:  26 February 2010

L. Carlitz ,
D. J. Lewis ,
W. H. Mills  and
E. G. Straus
L. Carlitz
Affiliation:
Duke University
D. J. Lewis
Affiliation:
University of Notre Dame
W. H. Mills
Affiliation:
Yale University
E. G. Straus
Affiliation:
University of California at Los Angeles
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Extract

Let p be a prime and let F be a polynomial in one variable with coefficients in GF(p), the field of p elements. Let d be the degree of F, and let r+1 denote the number of distinct values F(µ) as µ. ranges over GF(p). A generalization of the Waring problem modulo p leads to the question the determination of a lower bound for r.

Type
Research Article
Information
Mathematika , Volume 8 , Issue 2 , December 1961 , pp. 121 - 130
Copyright
Copyright © University College London 1961

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References

1. Chowla, S., Mann, H. B., and Straus, E. G., “Some applications of the Cauchy-Davenport theorem”, Norske Vid. Selsk. Forh. Trondheim, 32 (1959), 74–80.Google Scholar