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Search: MSC category 11L07 ( Estimates on exponential sums )

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1. CMB 2010 (vol 53 pp. 654)

Elliott, P. D. T. A.
 Variations on a Paper of ErdÅs and Heilbronn It is shown that an old direct argument of ErdÅs and Heilbronn may be elaborated to yield a result of the current inverse type. Categories:11L07, 11P70

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

3. CMB 1998 (vol 41 pp. 187)

Loh, W. K. A.
 Exponential sums on reduced residue systems The aim of this article is to obtain an upper bound for the exponential sums $\sum e(f(x)/q)$, where the summation runs from $x=1$ to $x=q$ with $(x,q)=1$ and $e(\alpha)$ denotes $\exp(2\pi i\alpha)$. We shall show that the upper bound depends only on the values of $q$ and $s$, %% where $s$ is the number of terms in the polynomial $f(x)$. Category:11L07