Revista Matemática Iberoamericana

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Volume 32, Issue 4, 2016, pp. 1127–1136
DOI: 10.4171/RMI/909

Published online: 2016-12-16

Polynomial values in small subgroups of finite fields

Igor E. Shparlinski[1]

(1) University of New South Wales, Sydney, Australia

For a large prime $p$, and a polynomial $f$ over a finite field $\mathbb F_p$ of $p$ elements, we obtain a lower bound on the size of the multiplicative subgroup of $\mathbb F_p^*$ containing $H \ \geq 1$ consecutive values $f(x), x = u+1, \ldots, u+H$, uniformly over $f \in \mathbb F_p[X]$ and an $u \in \mathbb F_p$.

Keywords: Polynomial congruences, finite fields

Shparlinski Igor: Polynomial values in small subgroups of finite fields. Rev. Mat. Iberoam. 32 (2016), 1127-1136. doi: 10.4171/RMI/909