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

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1. CMB Online first

Cook, Brian
 Discrete multilinear spherical averages In this note we give a characterization of $\ell^{p}\times \cdots\times \ell^{p}\to\ell^q$ boundedness of maximal operators associated to multilinear convolution averages over spheres in $\mathbb{Z}^n$. Keywords:discrete maximal function, multilinear averageCategories:11L07, 42B25

2. CMB 2016 (vol 59 pp. 592)

Liu, H. Q.
 The Dirichlet Divisor Problem of Arithmetic Progressions We design an elementary method to study the problem, getting an asymptotic formula which is better than Hooley's and Heath-Brown's results for certain cases. Keywords:Dirichlet divisor problem, arithmetic progressionCategories:11L07, 11B83

3. 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

4. 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

5. 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
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