Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Value sets of polynomials over finite fields

Authors: Da Qing Wan, Peter Jau-Shyong Shiue and Ching Shyang Chen
Journal: Proc. Amer. Math. Soc. 119 (1993), 711-717
MSC: Primary 11T06; Secondary 11T55
MathSciNet review: 1155603
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {{\mathbf{F}}_q}$ be the finite field of $ q$ elements, and let $ {V_f}$ be the number of values taken by a polynomial $ f(x)$ over $ {{\mathbf{F}}_q}$. We establish a lower bound and an upper bound of $ {V_f}$ in terms of certain invariants of $ f(x)$. These bounds improve and generalize some of the previously known bounds of $ {V_f}$. In particular, the classical Hermite-Dickson criterion is improved. Our bounds also give a new proof of a recent theorem of Evans, Greene, and Niederreiter. Finally, we give some examples which show that our bounds are sharp.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11T06, 11T55

Retrieve articles in all journals with MSC: 11T06, 11T55

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society