An estimate of Gaussian sums (Q1219910)
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scientific article; zbMATH DE number 3487545
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An estimate of Gaussian sums |
scientific article; zbMATH DE number 3487545 |
Statements
An estimate of Gaussian sums (English)
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1975
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By means of some complicated elementary considerations the author proves the inequality \[ \left|\sum_{k=0}^{q-1} e(\tfrac aq k^n)\right|\leq \exp\left(c\left(\tfrac {n}{\varphi(n)}\right)^2\right) \] uniformly in \(n,a\), and \(q\) \((n\geq 3,\;(a,q)=1)\). The importance of this result lies in the weak dependence of the upper bound on the parameter \(n\).
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