The ternary Goldbach problem in arithmetic progressions
Volume 82 / 1997
                    
                    
                        Acta Arithmetica 82 (1997), 197-227                    
                                        
                        DOI: 10.4064/aa-82-3-197-227                    
                                    
                                                Abstract
For a large odd integer N and a positive integer r, define b = (b₁,b₂,b₃) and $