Meromorphic Continuation of the Goldbach generating function

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

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

We consider the Dirichlet series associated to the number of representations of an integer as the sum of primes. Assuming the Riemann hypothesis on the distribution of the zeros of the Riemann zeta function we obtain the domain of meromorphic continuation of this series.

Mots clés: Goldbach numbers; circle method; meromorphic continuation

Domaines: Théorie des nombres [math.NT]

Gautami Bhowmik, Jan-Christoph Schlage-Puchta. Meromorphic Continuation of the Goldbach generating function. soumis, 2010, pp.1-10. ⟨hal-00459918⟩