Approximation of exponential sums by shorter ones
type: Item
instance of: scholarly article
title: Approximation of exponential sums by shorter ones
zbMATH Open document ID: 0648.10023
DOI: 10.1007/BF02837821
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11L03
zbMATH DE Number: 4057611
zbMATH Keywords: transformation formula
zbMATH Keywords: exponential sum
zbMATH Keywords: saddle-point method
author: Anatolii A. Karatsuba
MaRDI profile type: Publication
cites work: Q5803461
full work available at URL: https://doi.org/10.1007/bf02837821
OpenAlex ID: W1975636891
description: scientific article; zbMATH DE number 4057611