Resumen de Goldbach numbers represented by polynomials

Alberto Perelli

• Let N be a large positive real number. It is well known that almost all even integers in the interval [N, 2N] are Goldbach numbers, i.e. a sum of two primes. The same result also holds for short intervals of the form [N, N+H], see Mikawa [4], Perelli-Pintz [7] and Kaczorowski-Perelli-Pintz [3] for the choice of admissible values of H and the size of the exceptional set in several problems in this direction.

  One may ask if similar results hold for thinner sequences of integers in [N, 2N], of cardinality smaller than the upper bound for the exceptional set in the above problems. In this paper we deal with the polynomial case.