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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 PÃ³lya-Vinogradov and Burgess. These estimates are applied to obtain results on recurrence mod $p$ by special elements. Keywords:character sums, Bohr sets, finite fieldsCategories: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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