On Vinogradov's constant in Goldbach's ternary problem
type: Item
instance of: scholarly article
title: On Vinogradov's constant in Goldbach's ternary problem
zbMATH Open document ID: 0876.11047
author: Dmitrii Zinoviev
published in: Journal of Number Theory
publication date: 1997-08-17T00:00:00Z
review text: The author shows that under the assumption of the Generalized Riemann Hypothesis every odd integer greater than \(10^{20}\) can be written as a sum of three primes. The proof requires a careful numerical study of the exponential sum \[ S(\alpha) =\sum_{n>1} \Lambda(n) \exp(-2\pi i\alpha n-n/N). \] The best value hitherto (under GRH) was \(10^{32}\) [\textit{B. Lucke}, Zur Hardy-Littlewoodschen behandlung des Goldbachschen Problems. Göttingen: Math.-naturwiss. Diss. (1926; JFM 52.0167.02)]. The best unconditional constant is about \(10^{43.000}\) [\textit{J. Chen} and \textit{T. Wang}, Acta Math. Sin. 32, 702-718 (1989; Zbl 0695.10041)].
Mathematics Subject Classification ID: 11P32
zbMATH DE Number: 1048759
zbMATH Keywords: Vinogradov constant
zbMATH Keywords: ternary Goldbach problem
zbMATH Keywords: sum of three primes
zbMATH Keywords: exponential sum
zbMATH Keywords: JFM 52.0167.02
reviewed by: Dieter Wolke
MaRDI profile type: Publication
full work available at URL: jnth.1997.2141
OpenAlex ID: W1996368722
cites work: Q5844343
cites work: On odd Goldbach problem under general Riemann hypothesis
cites work: Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
DOI: 10.1006/JNTH.1997.2141
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description: scientific article; zbMATH DE number 1048759