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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Recent progress in the Goldbach problem
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by R. D. James PDF
Bull. Amer. Math. Soc. 55 (1949), 246-260
References
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  • A. A. Buchstab, Sur la décomposition des nombres pairs en somme de deux composantes dont chacune est formée d’un nombre borné de facteurs premiers, C. R. (Doklady) Acad. Sci. URSS (N.S.) 29 (1940), 544–548 (French). MR 0004263
    • 4. L. E. Dickson, History of the theory of numbers, vol. 1, New York, 1934. 5. T. Estermann, Eine neue Darstellung und neue Anwendungen der Viggo Brunschen Methode, J. Reine Angew. Math. vol. 168 (1932) pp. 106-116. 6. G. H. Hardy and J. E. Littlewood, Some problems of Partitio Numerorum III, Acta Math. vol. 44 (1922). 7. H. Heilbronn, E. Landau, and P. Scherk, Alle grossen ganzen Zahlen lassen sich als Summe von höchstens 71 Primzahlen darstellen, Časopis pro Pěstování Mathematiky a Fysiky vol. 65 (1936) pp. 117-141.
  • R. D. James, On the sieve method of Viggo Brun, Bull. Amer. Math. Soc. 49 (1943), 422–432. MR 8229, DOI 10.1090/S0002-9904-1943-07938-4
  • R. D. James and H. Weyl, Elementary note on prime number problems of Vinogradoff’s type, Amer. J. Math. 64 (1942), 539–552. MR 6745, DOI 10.2307/2371703
    • 10. A. Khintchine, Zur additive Zahlentheorie, Rec. Math. (Mat. Sbornik) vol. 39 (1932) pp. 27-34. 11. E. Landau, Vorlesungen über Zahlentheorie, vol. 1, Leipzig, 1927. 12. E. Landau, Die Goldbach Vermutung und der Schnirelmannsche Satz, Nach. Ges. Wiss. Göttingen (1930) pp. 255-276. 13. E. Landau, Über einige neuere Fortschritte der additiven Zahlentheorie, Cambridge, 1937.
  • U. V. Linnik, A new proof of the Goldbach-Vinogradow theorem, Rec. Math. [Mat. Sbornik] N.S. 19 (61) (1946), 3–8 (Russian, with English summary). MR 0018693
    • 15. A. Page, On the number of primes in an arithmetic progression, Proc. London Math. Soc. (2) vol. 39 (1935) pp. 116-141. 16. H. Rademacher, Beitrage zur Viggo Brunschen Methode in der Zahlentheorie, Abh. Math. Sem. Hamburgischen Univ. vol. 3 (1924) pp. 12-30. 17. G. Ricci, Sui grandi divisori primi delle coppie di interi in posti corrispondenti di due progressioni aritmetiche. Applicazione del metodo di Brun, Annali di Matematica Pura ed Applicata (4) vol. 11 (1932-1933). 18. G. Ricci, Ricerche aritmetiche sui polinomi, I, II, Rend. Circ. Mat. Palermo vol. 57 (1933), vol. 58 (1934). 19. G. Ricci, Su la congettura di Goldbach e la costante di Schnirelmann, Annali della R. Scuola Normale Superiore di Pisa (2) vol. 6 (1937). 20. L. Schnirelmann, Ob additiwnich swoistwach tschisel, Izvestiya Donskowo Polytechnitscheskowo Instituta (Nowotscherkask) vol. 14 (1930) pp. 3-28. 21. C. L. Siegel, Über die Classenzahl quadratischer Zahlkorper, Acta Arithmetica vol. 1 (1935) pp. 83-86.
  • N. Tchudakoff, On Goldbach-Vinogradov’s theorem, Ann. of Math. (2) 48 (1947), 515–545. MR 21021, DOI 10.2307/1969127
    • 23. I. M. Vinogradov, Some theorems concerning the theory of primes, Rec. Math. (Mat. Sbornik) N.S. vol. 2 (1937) pp. 179-195.
Additional Information
  • Journal: Bull. Amer. Math. Soc. 55 (1949), 246-260
  • DOI: https://doi.org/10.1090/S0002-9904-1949-09180-2
  • MathSciNet review: 0028893