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Mesures de transcendance et aspects quantitatifs de la méthode de Thue-Siegel-Roth-Schmidt
- Source :
- Proc. London Math. Soc., Proc. London Math. Soc., 2010, 101, pp.1--31. ⟨10.1112/plms/pdp054⟩
- Publication Year :
- 2010
- Publisher :
- HAL CCSD, 2010.
-
Abstract
- A proof of the transcendence of a real number ! based on the Thue‐Siegel‐Roth‐Schmidt method involves generally a sequence (" n)n! 1 of algebraic numbers of bounded degree or a sequence (xn)n! 1 of integer r-tuples. In the present paper, we show how such a proof can produce a transcendence measure for ! , if one is able to quantify the growth of the heights of the algebraic numbers " n or of the points xn. Our method rests on the quantitative Schmidt subspace theorem. We further give several applications, including to certain normal numbers and to the extremal numbers introduced by Roy.
- Subjects :
- Sequence
Pure mathematics
Subspace theorem
Degree (graph theory)
General Mathematics
010102 general mathematics
0102 computer and information sciences
01 natural sciences
Measure (mathematics)
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Combinatorics
Integer
010201 computation theory & mathematics
Bounded function
0101 mathematics
Algebraic number
ComputingMilieux_MISCELLANEOUS
Real number
Mathematics
Subjects
Details
- Language :
- French
- Database :
- OpenAIRE
- Journal :
- Proc. London Math. Soc., Proc. London Math. Soc., 2010, 101, pp.1--31. ⟨10.1112/plms/pdp054⟩
- Accession number :
- edsair.doi.dedup.....ba13a2f1063b10b7963a5f6a8d5670bd