Abstract

In this paper we shall be concerned with the question of the existence of Goldbach numbers in short intervals and the asymptotic formula for the number of representations of the even integers in a short interval as the sum of two primes. It was proven by Montgomery and Vaughan [MV2] that every interval (N- K,N] contains Goldbach numbers provided that K > N 7/72+e and N > No(e). More recently Perelli and Pintz [PP] have proven that almost every even integer in the interval (N- K, N] is a Goldbach number if

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