1. CMB 2015 (vol 58 pp. 774)
 Hanson, Brandon

Character Sums over Bohr Sets
We prove character sum estimates for additive Bohr subsets modulo
a prime.
These estimates are analogous to classical character sum bounds
of
PÃ³lyaVinogradov and Burgess. These estimates are applied to
obtain results on
recurrence mod $p$ by special elements.
Keywords:character sums, Bohr sets, finite fields Categories:11L40, 11T24, 11T23 

2. CMB 2001 (vol 44 pp. 87)
 Lieman, Daniel; Shparlinski, Igor

On a New Exponential Sum
Let $p$ be prime and let $\vartheta\in\Z^*_p$ be of
multiplicative order $t$ modulo $p$. We consider exponential
sums of the form
$$
S(a) = \sum_{x =1}^{t} \exp(2\pi i a \vartheta^{x^2}/p)
$$
and prove that for any $\varepsilon > 0$
$$
\max_{\gcd(a,p) = 1} S(a) = O( t^{5/6 + \varepsilon}p^{1/8}) .
$$
Categories:11L07, 11T23, 11B50, 11K31, 11K38 
