On the exceptional set for the sum of a prime and the \(k\)-th power of a prime
type: Item
instance of: scholarly article
zbMATH Open document ID: 0980.11047
author: C. Bauer
publication date: 2001-06-13T00:00:00Z
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 1604252
zbMATH Keywords: sum of a prime and \(k\)-th power of a prime
zbMATH Keywords: circle method
zbMATH Keywords: exceptional set
MaRDI profile type: Publication
title: On the exceptional set for the sum of a prime and the \(k\)-th power of a prime
published in: Studia Scientiarum Mathematicarum Hungarica
review text: The author proves that ``almost all'' integers which feasibly could be expressed as the sum of a prime and the \(k\)th power of a prime, actually can be so expressed. By ``almost all'' the author gives the surprisingly strong upper bound \(O_k(x^{1-\delta_k})\) for the number of exceptional \(n\) up to \(x\). The proof is modelled on \textit{H. L. Montgomery} and \textit{R. C. Vaughan}'s application of the circle method [Acta Arith. 27, 253-370 (1975; Zbl 0301.10043)] to the Goldbach problem (the case \(k=1\) here), though extensively modified, and also influenced by several papers that have appeared in the meantime.
reviewed by: Andrew Granville
description: scientific article; zbMATH DE number 1604252