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Search: MSC category 11T23 ( Exponential sums )

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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 Pólya-Vinogradov 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

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