Titlebook: Diophantine Approximation on Linear Algebraic Groups; Transcendence Proper Michel Waldschmidt Book 2000 Springer-Verlag Berlin Heidelberg 2

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书目名称Diophantine Approximation on Linear Algebraic Groups影响因子(影响力)




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书目名称Diophantine Approximation on Linear Algebraic Groups网络公开度学科排名




书目名称Diophantine Approximation on Linear Algebraic Groups被引频次




书目名称Diophantine Approximation on Linear Algebraic Groups被引频次学科排名




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书目名称Diophantine Approximation on Linear Algebraic Groups年度引用学科排名




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书目名称Diophantine Approximation on Linear Algebraic Groups读者反馈学科排名

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Book 2000tive version of which is also included. It yields new results of simultaneous approximation and of algebraic independence. 2 chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to P. Philippon) onlinear algebraic groups.

冬眠

0072-7830 c independence. 2 chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to P. Philippon) onlinear algebraic groups.978-3-642-08608-3978-3-662-11569-5Series ISSN 0072-7830 Series E-ISSN 2196-9701

名词

Introduction and Historical Surveyas well as in the nonhomogeneous version. We also describe the six exponentials Theorem, we present the state of the art on the problem of algebraic independence of logarithms of algebraic numbers. We conclude with a few comments on the Linear Subgroup Theorem.

Proponent

ciliary-body

Heights of Algebraic Numberslle’s inequality (§ 3.5) is an extension of these estimates and provides a lower bound for the absolute value of any nonzero algebraic number. More specifically, if we are given finitely many (fixed) algebraic numbers ..,...,.., and a polynomial . ∈ ℤ[X.,...,X.] which does not vanish at the point (.

ciliary-body

Zero Estimate, by Damien Royng is prescribed. This result takes into account the multidegrees of the obstruction subgroup and improves in this way the earlier zero estimates of D. W. Masser [Ma 1981b] and D. W. Masser and G. Wüstholz [MaWü 19811 A refinement will be given in Chap. 8 when multiplicities are introduced.

LAPSE

Flinch

Multiplicity Estimate by Damien Royally due to P. Philippon (see [P 1986a]) and again we restrict to commutative linear algebraic groups. This allows us to be more concrete and brings simplifications in the proof of the result. For an outline of the zero estimate of P. Philippon on a general commutative algebraic group, the reader ma

使人烦燥

On Baker’s Methodles. In Chapters 6 and 7, we extended Schneider’s method in several variables in order to prove the homogeneous transcendence result (Theorem 1.5) as well as quantitative refinements. The proofs did not involve any derivative at all. In Chap. 9, a single derivative was introduced, so that a second p