Bulletin (New Series) of the American Mathematical Society

A complete solution to the polynomial 3-primes problem

Gove W. Effinger and David R. Hayes

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Bull. Amer. Math. Soc. (N.S.), Volume 24, Number 2 (1991), 363-369.

First available in Project Euclid: 5 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11P32: Goldbach-type theorems; other additive questions involving primes 11T55: Arithmetic theory of polynomial rings over finite fields


Effinger, Gove W.; Hayes, David R. A complete solution to the polynomial 3-primes problem. Bull. Amer. Math. Soc. (N.S.) 24 (1991), no. 2, 363--369. https://projecteuclid.org/euclid.bams/1183656876

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  • 1. E. Artin, Geometric algebra, Interscience Publishers, New York, 1957.
  • 2. K. G. Borodzkin, K voprosu o postoyanni I. M. Vinogradov, Trudy tretego vsesoiuznogo matematiceskogo siezda 1 (1956), Moskva.
  • 3. M. Car, Le problem de Goldbach pour l'anneau des polynomes sur un corps fini, C. R. Acad. Sci. Paris Ser. A 273 (1971), 201-204.
  • 4. G. W. Effinger, A Goldbach theorem for polynomials of low degree over odd finite fields, Acta Arithmetica 42 (1983), 329-365.
  • 5. G. W. Effinger, A Goldbach 3-primes theorem for polynomials of low degree over finite fields of characteristic 2, J. Number Theory 29 (1988), 345-363.
  • 6. G. W. Effinger, The polynomial 3-primes conjecture, Computer Assisted Analysis and Modeling on the IBM 3090, MIT Press, Cambridge, MA. (to appear).
  • 7. G. W. Effinger and D. R. Hayes, Additive number theory of polynomials over a finite field, Oxford Univ. Press, England (to appear).
  • 8. G. H. Hardy and J. E. Littlewood, Some problems of 'partitio numerorum': On the expression of a number as a sum of primes, Acta Math. (Stockholm) 44 (1923), 1-70.
  • 9. D. R. Hayes, The distribution of irreducibles in GF[q, x], Trans. Amer. Math. Soc. 117 (1965), 101-127.
  • 10. D. R. Hayes, The expression of a polynomial as a sum of three irreducibles, Acta Arith. 11 (1966), 461-488.
  • 11. J. G. M. Mars, Sur l'approximation du nombre de solutions de certaines equations Diophantiennes, Ann. Sci. École Norm. Sup. 4e Ser. 6 (1973), 357-388.
  • 12. I. M. Vinogradov, Representation of an odd number as a sum of three primes, Comptes Rendues (Doklady) de l'Academy des Sciences de l'URSS, Tome 15 (1937), 191-294.