Goldbach numbers represented by polynomials

• Autores: Alberto Perelli
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 12, Nº 2, 1996, págs. 477-490
• Idioma: inglés
• DOI: 10.4171/rmi/205
• Títulos paralelos:
  • Números de Goldbach representados por polinomios.
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• Resumen

  • 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.