Binary problems. The spectral approach
type: Item
instance of: scholarly article
title: Binary problems. The spectral approach
zbMATH Open document ID: 1011.11063
DOI: 10.1007/BF02675730
author: A. I. Vinogradov
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-09-24T00:00:00Z
review text: The author's intention is to prove Goldbach's conjecture. In fact he claims he can prove an asymptotic formula for the number of representations of even integers \(2N\) as sums of two primes: \[ \sum_{2N= n_1+n_2} \Lambda(n_1) \Lambda(n_2)\sim \prod_{p\mid 2N} \biggl(1+ \frac{1}{n-1}\biggr) \prod_{p\nmid 2N} \biggl( 1- \frac{1}{(p-1)^2} \biggr)N. \] In this paper the problem is formulated in terms of the mean of Kloosterman sums. It is announced that in a second part this mean will be expressed in terms of spectral estimates that would lead to a solution.
reviewed by: Minggao Lu
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11L05
zbMATH DE Number: 1510524
zbMATH Keywords: binary Goldbach problem
zbMATH Keywords: Heisenberg noncommutativity
zbMATH Keywords: Möbius function
zbMATH Keywords: Kloosterman sums
MaRDI profile type: Publication
cites work: Q3248068
cites work: Kloosterman sums and Fourier coefficients of cusp forms
cites work: Topics in multiplicative number theory
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description: scientific article; zbMATH DE number 1510524