D. A. Goldston, Liyang Yang
Published 2016-01-26Version 1
Assuming the Riemann Hypothesis, we obtain asymptotic formulas for the average number representations of an even integer as the sum of two primes. We use the method of Bhowmik and Schlage-Puchta and refine their results slightly to obtain a more recent result of Languasco and Zaccagnini, and a new result on a smoother average.
The average number of Goldbach representations over multiples of $q$
On a smoothed average of the number of Goldbach representations
Explicit formulae for averages of Goldbach representations
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