The Hilbert polynomial and linear forms in the logarithms of algebraic numbers

被引：10
|
作者：
Aleksentsev, Yu. M. [1 ]
机构：
[1] Technol Univ, Moscow State Inst Steel & Alloys, Moscow, Russia
来源：
IZVESTIYA MATHEMATICS | 2008年 / 72卷 / 06期
关键词：
D O I：
10.1070/IM2008v072n06ABEH002429
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We. prove a new estimate for homogeneous linear forms with integer coefficients in the logarithms of algebraic numbers. We obtain a qualitative improvement, of the estimate depending oil the coefficients of the linear form and the best value of the constant ill the estimate in the, case when the number of logarithms is not too large.
引用
收藏
页码：1063 / 1110
页数：48
相关论文
共 50 条
  • [41] On the linear independence measure of logarithms of rational numbers
    Wu, Q
    MATHEMATICS OF COMPUTATION, 2003, 72 (242) : 901 - 911
  • [42] Polynomial Computability of Fields of Algebraic Numbers
    P. E. Alaev
    V. L. Selivanov
    Doklady Mathematics, 2018, 98 : 341 - 343
  • [43] Polynomial Computability of Fields of Algebraic Numbers
    Alaev, P. E.
    Selivanov, V. L.
    DOKLADY MATHEMATICS, 2018, 98 (01) : 341 - 343
  • [44] Linear forms in two logarithms and interpolation determinants
    Laurent, M
    Mignotte, M
    Nesterenko, Y
    JOURNAL OF NUMBER THEORY, 1995, 55 (02) : 285 - 321
  • [45] Recent progress on linear forms in elliptic logarithms
    David, S
    Hirata-Kohno, N
    PANORAMA IN NUMBER THEORY OR THE VIEW FROM BAKER'S GARDEN, 2002, : 26 - 37
  • [46] Measures of linear independance of logarithms in a commutative algebraic group
    Gaudron, É
    INVENTIONES MATHEMATICAE, 2005, 162 (01) : 137 - 188
  • [47] Linear independence measure of logarithms on a commutative algebraic group
    Gaudron, T
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (12): : 1059 - 1064
  • [48] Linear forms of effective logarithms on abelian varieties
    Gaudron, Eric
    ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2006, 39 (05): : 699 - 773
  • [49] LINEAR FORMS IN 2 LOGARITHMS AND SCHNEIDERS METHOD
    MIGNOTTE, M
    WALDSCHMIDT, M
    MATHEMATISCHE ANNALEN, 1978, 231 (03) : 241 - 267
  • [50] Hilbert type numbers for polynomial ODE's
    Calanchi, M
    Ruf, B
    NONLINEAR EQUATIONS: METHODS, MODELS AND APPLICATIONS, 2003, 54 : 53 - 60
12345