No abstract

Abstract. 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 Ω-term, we show that our result is essentially the best possible.

This article extends classical one variable results about Euler products defined by integral valued polynomial or analytic functions to several variables. We show there exists a meromorphic continuation up to a presumed natural boundary, and also give a criterion, a la Estermann-Dahlquist, for the existence of a meromorphic extension to C n . Among applications we deduce analytic properties of height zeta functions for toric varieties over Q and group zeta functions.Mathematics Subject Classifications: 11M41, 11N37, 14G05, 32D15.