Linear equations over \(\mathbb F_ p\) and moments of exponential sums.
type: Item
instance of: scholarly article
title: Linear equations over \(\mathbb F_ p\) and moments of exponential sums.
zbMATH Open document ID: 1035.11007
DOI: 10.1215/S0012-7094-01-10722-9
published in: Duke Mathematical Journal
publication date: 2002-10-27T00:00:00Z
review text: The author obtains an \(\mathbb{F}_p\) analogue of the rearrangement theorems due to Gabriel, Hardy and Littlewood in the version given by the author [J. Comb. Theory, Ser. A 83, 251--267 (1998; Zbl 0907.11009)]. The original ``integral'' version follows from the \(\mathbb{F}_p\) version. He also obtains new estimates, a set \(A\) of residues modulo \(p\) being given, on the number of \(x\in \mathbb{Z}/p\mathbb{Z}\) such that \(\sum_{a\in A}\exp(2\pi iax/p)\) is ``large''. The result obtained can be seen as an \(\mathbb{F}_p\) analogue of a result by \textit{A. A. Yudin} [Teoretiko-Chisl. Issled. Spektru Markov. Struktur. Teor. Slozhen. Mnozhestv, 163--161 (1973; Zbl 0321.10047)].
reviewed by: Alain Plagne
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 11D04
Mathematics Subject Classification ID: 11L07
Mathematics Subject Classification ID: 42C20
zbMATH DE Number: 1820801
zbMATH Keywords: rearrangement theorems
zbMATH Keywords: exponential sums
zbMATH Keywords: \(\mathbb{F}_p\)-analog
author: Vsevolod F. Lev
MaRDI profile type: Publication
cites work: The Rearrangement of Positive Fourier Coefficients
cites work: On the number of solutions of a linear equation over finite sets
cites work: Addition Properties of Residue Classes
full work available at URL: s0012-7094-01-10722-9
OpenAlex ID: W1480351579
description: scientific article; zbMATH DE number 1820801