Mean representation number of integers as the sum of primes

Gautami Bhowmik (1) , Jan-Christoph Schlage-Puchta (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Mathematisches institut

Assuming the Riemann Hypothesis we obtain asymptotic estimates for the mean value of the number of representations of an integer as a sum of two primes. By proving a corresponding Omega-term, we prove that our result is essentially the best possible.

Mots clés: Goldbach numbers; asymptotic order

Domaines: Théorie des nombres [math.NT]

Gautami Bhowmik, Jan-Christoph Schlage-Puchta. Mean representation number of integers as the sum of primes. Nagoya Mathematical Journal, 2010, pp.0-6. ⟨hal-00289430v3⟩