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On a New Exponential Sum |
Published:2001-03-01
Printed: Mar 2001
Printed: Mar 2001
- Daniel Lieman
- Igor Shparlinski
Abstract
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 $\varepsilon > 0$
$$
\max_{\gcd(a,p) = 1} |S(a)| = O( t^{5/6 + \varepsilon}p^{1/8}) .
$$
| MSC Classifications: |
11L07 - Estimates on exponential sums 11T23 - Exponential sums 11B50 - Sequences (mod $m$) 11K31 - Special sequences 11K38 - Irregularities of distribution, discrepancy [See also 11Nxx] |