Goldbach's problem
type: Item
instance of: scholarly article
title: Goldbach's problem
zbMATH Open document ID: 0805.11003
DOI: 10.1007/BF03186499
published in: Mathematische Semesterberichte
publication date: 1995-02-05T00:00:00Z
review text: The author presents a historical survey on Goldbach's problem, i.e. the representation of integers as sums of two or three primes. He sketches the Hardy-Littlewood circle method and the results obtained from it, I. M. Vinogradov's solution of the ternary Goldbach problem, the implications of sieve methods, and more recent results (for example the estimate of Montgomery-Vaughan for the number of exceptional, non- Goldbach-integers), localized forms on the ternary problem, the deep Heath-Brown hypothetical result (prime twins and Siegel zeros) and others. Finally some open problems are mentioned.
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11P55
Mathematics Subject Classification ID: 01-02
Mathematics Subject Classification ID: 11N35
Mathematics Subject Classification ID: 11M20
zbMATH DE Number: 575608
zbMATH Keywords: binary Goldbach problem
zbMATH Keywords: Riemann hypothesis
zbMATH Keywords: Siegel zeros
zbMATH Keywords: density theorems
zbMATH Keywords: sums of two primes
zbMATH Keywords: sums of three primes
zbMATH Keywords: exceptional set
zbMATH Keywords: prime twins
zbMATH Keywords: historical survey
zbMATH Keywords: Goldbach's problem
zbMATH Keywords: representation of integers
zbMATH Keywords: Hardy-Littlewood circle method
zbMATH Keywords: ternary Goldbach problem
zbMATH Keywords: sieve methods
author: Dieter Wolke
reviewed by: Wolfgang Schwarz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 575608