On the number of solutions of \(N-p=P_ 3\) (Q788765)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the number of solutions of \(N-p=P_ 3\) |
scientific article; zbMATH DE number 3843847
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of solutions of \(N-p=P_ 3\) |
scientific article; zbMATH DE number 3843847 |
Statements
On the number of solutions of \(N-p=P_ 3\) (English)
0 references
1984
0 references
Let N be an even positive integer and define \[ C_ N=\prod_{p>2}(1- 1/(p-1)^ 2)\prod_{2<p| N}(p-1)/(p-2). \] \textit{H.-E. Richert} [Mathematika 16, 1-22 (1969; Zbl 0192.397)] proved that if N is sufficiently large then \[ | \{p:\quad p<N,\quad N-p=P_ 3\}| \quad>\quad(13/3) C_ N (N/\log^ 2N). \] In this paper, the constant 13/3 is improved to 6.173. The proof uses mean value theorems of the Bombieri-Vinogradov type and Chen's ''switching'' argument, but it does not use sieve weights.
0 references
representations of integers
0 references
sum of prime and almost prime
0 references
application of sieve methods
0 references
mean value theorems of Bombieri-Vinogradov type
0 references
Chen switching argument
0 references
