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On a New Exponential Sum

Open Access article
 Printed: Mar 2001
  • Daniel Lieman
  • Igor Shparlinski
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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, 11T23, 11B50, 11K31, 11K38 show english descriptions Estimates on exponential sums
Exponential sums
Sequences (mod $m$)
Special sequences
Irregularities of distribution, discrepancy [See also 11Nxx]
11L07 - Estimates on exponential sums
11T23 - Exponential sums
11B50 - Sequences (mod $m$)
11K31 - Special sequences
11K38 - Irregularities of distribution, discrepancy [See also 11Nxx]

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