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

作者：Suzuki Yuta^*

来源：International Journal of Number Theory, 2017, 13(4): 977-990.

DOI：10.1142/S1793042117500518

• Goldbach conjecture
• arithmetic progressions
• mean value
• circle method

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. Ruppel in 2009, and a generalization of the result of A. Languasco and A. Zaccagnini concerning the ordinary Goldbach problem in 2012.

• 出版日期2017-5