A COMMENT ON GOLDBACH'S CONJECTURE

  • Mozzochi, C.J. (Institut Mittag-Leffler The Royal Swedish Academy of Sciences)
  • 발행 : 1979.12.20

초록

No matter how one chooses the major arcs in the decomposition of $[x_0,\;x_0+1]$ it is always true with regard to the union, m(n), of the corresponding minor arcs that the integal of $f^2(x,\;n)$ e(-nx) over m(n) is $O(nlog^{-1}n)$. Consequently, to establish a proof of the asymptotic formulation of Goldbach's conjecture one might be tempted to take this fact as a starting point and to then concentrate the attact on trying to obtain the requisite estimate on the integral of $f^2(x,\;n)$ e(-nx) over M(n), the union of a suitably chosen family of major arcs. In this paper I show that this approach is not possible.

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