- journal article metadata
European Mathematical Society Publishing House
2016-12-19 23:45:00
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
32
2016
4
Polynomial values in small subgroups of finite fields
Igor
Shparlinski
University of New South Wales, SYDNEY, NSW, AUSTRALIA
Polynomial congruences, finite fields
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 $u \in \mathbb F_p$.
Number theory
1127
1136
10.4171/RMI/909
http://www.ems-ph.org/doi/10.4171/RMI/909