Ebook: Introduction to Algebraic Independence Theory

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.

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A text presenting the results of research in algebraic independence theory in four parts, which include the latest results obtained for modular functions and modular forms; the necessary tools from commutative algebra; zero estimates and their role; and applications of the tools developed to this point. Softcover.