A complete solution to the polynomial 3-primes problem
HTML articles powered by AMS MathViewer
- by Gove W. Effinger and David R. Hayes PDF
- Bull. Amer. Math. Soc. 24 (1991), 363-369
References
- E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463 2. K. G. Borodzkin, K voprosu o postoyanni I. M. Vinogradov, Trudy tretego vsesoiuznogo matematiceskogo siezda 1 (1956), Moskva.
- Mireille Car, Le problème de Goldbach pour l’anneau des polynômes sur un corps fini, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A201–A204 (French). MR 282938
- Gove Effinger, A Goldbach theorem for polynomials of low degree over odd finite fields, Acta Arith. 42 (1983), no. 4, 329–365. MR 736718, DOI 10.4064/aa-42-4-329-365
- Gove Effinger, A Goldbach $3$-primes theorem for polynomials of low degree over finite fields of characteristic $2$, J. Number Theory 29 (1988), no. 3, 345–363. MR 955958, DOI 10.1016/0022-314X(88)90111-4 6. G. W. Effinger, The polynomial 3-primes conjecture, Computer Assisted Analysis and Modeling on the IBM 3090, MIT Press, Cambridge, MA. (to appear).
- Gove W. Effinger and David R. Hayes, Additive number theory of polynomials over a finite field, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1143282
- G. H. Hardy and J. E. Littlewood, Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes, Acta Math. 44 (1923), no. 1, 1–70. MR 1555183, DOI 10.1007/BF02403921
- David R. Hayes, The distribution of irreducibles in $\textrm {GF}[q,\,x]$, Trans. Amer. Math. Soc. 117 (1965), 101–127. MR 169838, DOI 10.1090/S0002-9947-1965-0169838-6
- D. R. Hayes, The expression of a polynomial as a sum of three irreducibles, Acta Arith. 11 (1966), 461–488. MR 201422, DOI 10.4064/aa-11-4-461-488
- J. G. M. Mars, Sur l’approximation du nombre de solutions de certaines équations diophantiennes, Ann. Sci. École Norm. Sup. (4) 6 (1973), 357–387. MR 432574, DOI 10.24033/asens.1251 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.
Additional Information
- Journal: Bull. Amer. Math. Soc. 24 (1991), 363-369
- MSC (1985): Primary 11P32, 11T55
- DOI: https://doi.org/10.1090/S0273-0979-1991-16035-0
- MathSciNet review: 1069987