数论 Ⅳ 超越数 Number theory Ⅳ Transcendental numbers numbers A. N. Parshin 科学出版社 PDF电子教材 PDF电子书 大学教材电子版 电子课本 网盘下载【高清非扫描版】

国外数学名著系列《数论 Ⅳ 超越数 Number theory Ⅳ Transcendental numbers numbers》A. N. Parshin 科学出版社 PDF电子教材 PDF电子书 大学教材电子版 电子课本 网盘下载【高清非扫描版】

图书简介：

This book is a survey of the most important directions of research in transcendental number theory. The central topics in this theory include proofs of irrationality and transcendence of various numbers，especially those that arise as the values of special functions. Questions of this sort go back to ancient times. An example is the old problem of squaring the circle，which Lindemann showed to be impossible in 1882，when he proved that Pi is a transcendental number. Euler’s conjecture that the logarithm of an algebraic number to an algebraic base is transcendental was included in Hilbert’s famous list of open problems; this conjecture was proved by Gel’fond and Schneider in 1934. A more recent result was Apéry’s surprising proof of the irrationality of ζ(3) in 1979.
The quantitative aspects of the theory have important applications to the study of Diophantine equations and other areas of number theory. For a reader interested in different branches of number theory，this monograph provides both an overview of the central ideas and techniques of transcendental number theory，and also a guide to the most important results and references.