Approximation of exponential sums by shorter ones
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.
scientific article; zbMATH DE number 4057611