On a new exponential sum (Q2739254)
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scientific article; zbMATH DE number 1643716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a new exponential sum |
scientific article; zbMATH DE number 1643716 |
Statements
27 June 2002
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exponential sums
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estimates
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On a new exponential sum (English)
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Let \(p\) be a prime, and let \(v\in \mathbb{Z}_p^*\) be an element of multiplicative order \(t\) modulo \(p\). The exponential sum NEWLINE\[NEWLINES(a)= \sum_{x=1}^t \exp(2\pi i\nu^{x^2}/p)NEWLINE\]NEWLINE is considered. The main result is the proof that NEWLINE\[NEWLINE\max_{\text{gcd}(a,p)=1} |S(a)|= O(t^{5/6+\varepsilon} p^{1/8}).NEWLINE\]
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