Introduction to Algebraic Independence Theory

• Corporate Author: SpringerLink (Online service)
• Other Authors: Nesterenko, Yuri V. (Editor, http://id.loc.gov/vocabulary/relators/edt), Philippon, Patrice (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 1st ed. 2001.
• Series: Lecture Notes in Mathematics, 1752
• Subjects: Number theory.; Algebraic geometry.; Number Theory.; Algebraic Geometry.
• Physical Description: XVI, 260 p. online resource.
• ISBN: 9783540445500
• ISSN: 0075-8434 ;
• DOI: 10.1007/b76882

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.