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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Local Diophantine Nullstellen inequalities
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by W. Dale Brownawell
J. Amer. Math. Soc. 1 (1988), 311-322
DOI: https://doi.org/10.1090/S0894-0347-1988-0928261-3
References
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  • W. Dale Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of Math. (2) 126 (1987), no. 3, 577–591. MR 916719, DOI 10.2307/1971361
  • W. Dale Brownawell, Large transcendence degree revisited. I. Exponential and non-CM cases, Diophantine approximation and transcendence theory (Bonn, 1985) Lecture Notes in Math., vol. 1290, Springer, Berlin, 1987, pp. 149–173. MR 927560, DOI 10.1007/BFb0078707
  • W. Dale Brownawell, Note on a paper of P. Philippon: “Zero estimates in commutative algebraic groups” [Bull. Soc. Math. France 114 (1986), no. 3, 355–383], Michigan Math. J. 34 (1987), no. 3, 461–463. MR 911818, DOI 10.1307/mmj/1029003625
  • W. Dale Brownawell and Robert Tubbs, Large transcendence degree revisited. II. The CM case, Diophantine approximation and transcendence theory (Bonn, 1985) Lecture Notes in Math., vol. 1290, Springer, Berlin, 1987, pp. 175–188. MR 927561, DOI 10.1007/BFb0078708
  • Gregory V. Chudnovsky, Some analytic methods in the theory of transcendental numbers, Contributions to the theory of transcendental numbers, Math. Surveys Monogr., vol. 19, Amer. Math. Soc., Providence, RI, 1984, pp. 27–122. Translated from the Russian by G. A. Kandall. MR 772029, DOI 10.1090/surv/019/02
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  • D. W. Masser and G. Wüstholz, Fields of large transcendence degree generated by values of elliptic functions, Invent. Math. 72 (1983), no. 3, 407–464. MR 704399, DOI 10.1007/BF01398396
  • Ju. V. Nesterenko, Estimate of the orders of the zeroes of functions of a certain class, and their application in the theory of transcendental numbers, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), no. 2, 253–284, 477 (Russian). MR 0491535
  • Yu. V. Nesterenko, Estimates for the characteristic function of a prime ideal, Mat. Sb. (N.S.) 123(165) (1984), no. 1, 11–34 (Russian). MR 728927
  • Yu. V. Nesterenko, Algebraic independence of algebraic powers of algebraic numbers, Mat. Sb. (N.S.) 123(165) (1984), no. 4, 435–459 (Russian). MR 740672
  • Yu. V. Nesterenko, The measure of algebraic independence of values of certain functions, Mat. Sb. (N.S.) 128(170) (1985), no. 4, 545–568, 576 (Russian). MR 820402
  • Patrice Philippon, Critères pour l’indépendance algébrique, Inst. Hautes Études Sci. Publ. Math. 64 (1986), 5–52 (French). MR 876159
  • —, Sur les mesures d’indépendance algébrique, Séminaire de Théorie des Nombres, Boston-Basel-Stuttgart, Birkhäuser, 1985, pp. 219-233. —, Elimination effective, Journées Algorithmiques-Arithmétiques, Chap. XXVIII, Publ. Univ. St. Etienne, France, 1983.
  • Patrice Philippon, Lemmes de zéros dans les groupes algébriques commutatifs, Bull. Soc. Math. France 114 (1986), no. 3, 355–383 (French, with English summary). MR 878242
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Bibliographic Information
  • © Copyright 1988 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 1 (1988), 311-322
  • MSC: Primary 11J85; Secondary 13F20
  • DOI: https://doi.org/10.1090/S0894-0347-1988-0928261-3
  • MathSciNet review: 928261