On twisted character sums
type: Item
instance of: scholarly article
title: On twisted character sums
zbMATH Open document ID: 1284.11114
author: Fernando Chamizo
published in: Archiv der Mathematik
publication date: 2011-06-17T00:00:00Z
review text: Let \(p\) be a prime, and let \(\chi\) be a non-principal character modulo \(p\). Let \(f\) be a smooth \(1\)-periodic function and \(\alpha\in \mathbb{R}\), and let \(M,N,r\) be positive integers with \(M,N<p\) and \(r>1\). This paper proved that \[ \sum_{M<n\leq M+N}f(\alpha n)\chi(n)\ll ||f||_{2,1} N^{1-1/r}p^{1/(4r-4)}(\log p)^{1/2r}, \] where \(||f||_{2,1}=\int_{0}^{1}\left(|f|+|f''|\right)\) and the \(\ll\)-constant is absolute.
Mathematics Subject Classification ID: 11L05
Mathematics Subject Classification ID: 11L40
zbMATH DE Number: 5909099
zbMATH Keywords: character sums
zbMATH Keywords: Burgess estimate
MaRDI profile type: Publication
full work available at URL: s00013-011-0255-0
OpenAlex ID: W2011116647
cites work: On Character Sums and L -Series. II
cites work: Mean values of character sums
cites work: Partial Gaussian Sums
cites work: Q4830109
cites work: Q4674810
cites work: Q4327355
DOI: 10.1007/S00013-011-0255-0
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description: scientific article; zbMATH DE number 5909099