Abstract
Let E(X) denote the number of natural numbers not exceeding X which cannot be written as a sum of a prime and a square. In this paper we show that for sufficiently large X we have E(X)<< X0.982.
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R. Brünner, A. Perelli and J. Pintz, The exceptional set for the sum of a prime and a square, Acta Math. Hungar. 53 (1989), 347-365.
H. Davenport and H. Heilbronn, Note on a result in the additive theory of numbers, Proc. London Math. Soc. 43 (1937), 142-151.
G. H. Hardy and J. E. Littlewood, Some problems of partitio numerorum III: on the expression of a large number as a sum of primes, Acta Math. 44 (1923), 1-70.
M. Jutila, On Linnik's constant, Math Scand. 41 (1977), 45-62.
Hongze Li, Zero-free regions for Dirichlet L-functions, Quart. J. Math. Oxford 50 (1999), 13-23.
Hongze Li, The exceptional set of Goldbach numbers (II), Acta Arith. 92 (2000), 71-88.
Hongze Li, The number of powers of 2 in representations of large even integers by sums of such powers and of two primes, Acta Arith. 92 (2000), 229-237.
R. J. Miech, On the equation n = p + x 2, Trans. Amer. Math. Soc. 130 (1968), 494-512.
H. L. Montgomery and R. C. Vaughan, The exceptional set in Goldbach's problem, Acta Arith. 27 (1975), 353-370.
Chengdong Pan and Chengbiao Pan, Goldbach Conjecture (English version), Science Press (Beijing, 1992).
Tianze Wang, On the Exceptional Set for the Equation n = p + k 2, Acta Mathematica Sinica, New Series 11 (1995), 156-167.
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Hongze, L. The exceptional set for the sum of a prime and a square. Acta Mathematica Hungarica 99, 123–142 (2003). https://doi.org/10.1023/A:1024513613734
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DOI: https://doi.org/10.1023/A:1024513613734