Approximation of exponential sums by shorter ones (Q1104965)
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scientific article; zbMATH DE number 4057611
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of exponential sums by shorter ones |
scientific article; zbMATH DE number 4057611 |
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Approximation of exponential sums by shorter ones (English)
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1987
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The main result of the paper is a transformation formula with a good error term for the exponential sum \(\sum_{a\leq x\leq b}\phi (x)\exp (2\pi if(x))\). This is proved by the saddle-point method assuming that the derivatives \(\phi^{(i)}(x)\) and \(f^{(j)}(x)\) for \(i\leq 2\) and \(2\leq j\leq 4\) satisfy certain inequalities.
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transformation formula
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exponential sum
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saddle-point method
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