Dewey Class |
512.7 |
Title |
Introduction to Algebraic Independence Theory ([EBook] /) / edited by Yuri V. Nesterenko, Patrice Philippon. |
Added Personal Name |
Nesterenko, Yuri V. editor. |
Philippon, Patrice editor. |
Other name(s) |
SpringerLink (Online service) |
Publication |
Berlin, Heidelberg : : Springer Berlin Heidelberg, , 2001. |
Physical Details |
XVI, 260 p. : online resource. |
Series |
Lecture Notes in Mathematics 0075-8434 ; ; 1752 |
ISBN |
9783540445500 |
Summary Note |
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.: |
Contents note |
?(?, z) and Transcendence -- Mahler’s conjecture and other transcendence Results -- Algebraic independence for values of Ramanujan Functions -- Some remarks on proofs of algebraic independence -- Elimination multihomogene -- Diophantine geometry -- Géométrie diophantienne multiprojective -- Criteria for algebraic independence -- Upper bounds for (geometric) Hilbert functions -- Multiplicity estimates for solutions of algebraic differential equations -- Zero Estimates on Commutative Algebraic Groups -- Measures of algebraic independence for Mahler functions -- Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees -- Algebraic Independence in Algebraic Groups. Part II: Large Transcendence Degrees -- Some metric results in Transcendental Numbers Theory -- The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence. |
System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
Internet Site |
http://dx.doi.org/10.1007/b76882 |
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