On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II

R. Nair

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We show that for almost all $n \in N$ , the inequality $| p_{1} + p_{2} - \exp ((\log n)^{γ}) | < 1$ has solutions with odd prime numbers $p_{1}$ and $p_{2}$ , provided $1 < γ < \frac{3}{2}$ . Moreover, we give a rather sharp bound for the exceptional set. This result provides almost-all results for Goldbach numbers in sequences rather thinner than the values taken by any polynomial.

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