Introduction to Algebraic Independence Theory
Editors: Nesterenko, Yuri V., Philippon, Patrice (Eds.)
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- About this book
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In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
- Table of contents (16 chapters)
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Θ(τ, z) and Transcendence
Pages 1-11
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Mahler’s conjecture and other transcendence Results
Pages 13-26
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Algebraic independence for values of Ramanujan Functions
Pages 27-46
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Some remarks on proofs of algebraic independence
Pages 47-51
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Elimination multihomogene
Pages 53-81
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Table of contents (16 chapters)
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- URL of Patrice Philippon
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Introduction to Algebraic Independence Theory
- Editors
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- Yuri V. Nesterenko
- Patrice Philippon
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 1752
- Copyright
- 2001
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-44550-0
- DOI
- 10.1007/b76882
- Softcover ISBN
- 978-3-540-41496-4
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- XVI, 260
- Topics
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