| 词条 | 数论4:超越数 |
| 释义 | 图书信息出版社: 科学出版社; 第1版 (2009年1月1日) 外文书名: Number Theory Ⅳ: Transcendental Numbers 丛书名: 国外数学名著系列（续一）（影印版）65 精装: 345页 正文语种: 英语 开本: 16 ISBN: 9787030235084 条形码: 9787030235084 尺寸: 24 x 17.2 x 2.2 cm 重量: 680 g 作者简介作者：(俄罗斯)帕尔申 (Parshin.A.N.) (俄罗斯)I.R.Shafarevich 内容简介《数论4:超越数(影印版)》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 bc impossible in 1882，when hc proved that Pi is a trandental 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 Anerv's surprising proof of the irrationality of ξ(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. |
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