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1. CMB 2010 (vol 53 pp. 654)
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Variations on a Paper of ErdÅs and Heilbronn It is shown that an old direct argument of ErdÅs and Heilbronn may be elaborated to yield a result of the current inverse
type.
Categories:11L07, 11P70 |
2. CMB 2001 (vol 44 pp. 87)
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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)
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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 |