Lecture Notes in Mathematics

Nesterenko, Yuri V.; Amoroso, F.; Philippon, Patrice; Bertrand, D.; Brownawell, W.D.; Diaz, G.; Laurent, M.; Nesterenko, Yu.V.; Nishioka, K.; Philippon, P.; Remond, G.; Roy, D.; Waldschmidt, M.

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.

Details

Published by: Springer

Publication Date: 2001-01-18

Format: Paperback

ISBN-13: 9783540414964

DOI: 10.1007/b76882

Dimensions: 235cm x155cm

Pages: 260