The exceptional set of Goldbach numbers (II)
Hongze Li
Acta Arithmetica, Tome 92 (2000), p. 71-88 / Harvested from The Polish Digital Mathematics Library

1. Introduction. A positive number which is a sum of two odd primes is called a Goldbach number. Let E(x) denote the number of even numbers not exceeding x which cannot be written as a sum of two odd primes. Then the Goldbach conjecture is equivalent to proving that E(x) = 2 for every x ≥ 4. E(x) is usually called the exceptional set of Goldbach numbers. In [8] H. L. Montgomery and R. C. Vaughan proved that E(x)=O(x1-Δ) for some positive constant Δ > 0.In[3]ChenandPanprovedthatonecantakeΔ>0.01.In[6],weprovedthatE(x)=O(x0.921). In this paper we prove the following result. Theorem. For sufficiently large x, E(x)=O(x0.914). Throughout this paper, ε always denotes a sufficiently small positive number that may be different at each occurrence. A is assumed to be sufficiently large, A < Y, and D=Y1+ε.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:207370
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     author = {Hongze Li},
     title = {The exceptional set of Goldbach numbers (II)},
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     pages = {71-88},
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Hongze Li. The exceptional set of Goldbach numbers (II). Acta Arithmetica, Tome 92 (2000) pp. 71-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav92i1p71bwm/

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