The Ternary Goldbach Problem with Primes in Arithmetic Progressions

2001 ◽  
Vol 17 (4) ◽  
pp. 679-696 ◽  
Author(s):  
Zhen Feng Zhang ◽  
Tian Ze Wang
Keyword(s):  
Arithmetic Progressions ◽  
Goldbach Problem ◽  
Primes In Arithmetic Progressions ◽  
Ternary Goldbach Problem

scholarly journals A mean value of the representation function for the sum of two primes in arithmetic progressions

2017 ◽  
Vol 13 (04) ◽  
pp. 977-990 ◽  
Author(s):  
Yuta Suzuki
Keyword(s):  
Asymptotic Formula ◽  
Riemann Hypothesis ◽  
Mean Value ◽  
Arithmetic Progressions ◽  
Representation Function ◽  
Real Zeros ◽  
Generalized Riemann Hypothesis ◽  
Goldbach Problem ◽  
Primes In Arithmetic Progressions ◽  
The Mean

In this paper, assuming a variant of the Generalized Riemann Hypothesis, which does not exclude the existence of real zeros, we prove an asymptotic formula for the mean value of the representation function for the sum of two primes in arithmetic progressions. This is an improvement of the result of F. Rüppel in 2009, and a generalization of the result of A. Languasco and A. Zaccagnini concerning the ordinary Goldbach problem in 2012.

scholarly journals The ternary Goldbach problem in arithmetic progressions

1997 ◽  
Vol 82 (3) ◽  
pp. 197-227 ◽  
Author(s):  
Jianya Liu ◽  
Tao Zhan
Keyword(s):  
Arithmetic Progressions ◽  
Goldbach Problem ◽  
Ternary Goldbach Problem
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