Binary problems. The spectral approach
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.
scientific article; zbMATH DE number 1510524