Ivan Niven, Diophantine Approximations (Interscience Tracts in Pure and Applied Mathematics, No. 14, John Wiley & Sons, New York), viii+68 pp., 36s.
Ivan Niven, Diophantine Approximations (Interscience Tracts in Pure and Applied Mathematics, No. 14, John Wiley & Sons, New York), viii+68 pp., 36s.
复制标题
伊万·尼文 (Ivan Niven)，丢番图近似（《纯粹与应用数学交叉科学》，第 14 期，约翰·威利
DOI：
10.1017/s0013091500025748
复制
发表时间：
1963
影响因子：
0.7
通讯作者：
J. Hunter
中科院分区：
文献类型：
--
作者：
J. Hunter
NIVEN，IVAN，丢番图近似法（纯数学和应用数学中的跨科学Tracts，第14号，John Wiley & Sons，纽约），viii+68页，36秒这本小有吸引力的书出现了一个课程的讲座由作者在1960年夏季会议的美国数学协会。它给出了关于真实的和复数的齐次和非齐次逼近的基本结果的证明，真实的情况在第1章和第2章中考虑，而复数的类似情况在第4章和第5章中考虑。剩下的章节主要包含标准的结果分数和整数部分的序列的倍数的一个真实的数，其中许多是有关均匀分布。给出的证明完全避免使用连续分数;其中许多是新的和优雅的，但是，主要是因为困难的问题，并不是所有的简单，因为他们的外观会建议。除了列入通常被忽视的基本结果近似在复杂的情况下，最有用的特点，这本书的评论和事实载于题为“进一步的结果“的章节结束时，广泛和最新的参考书目。这本书是，其规模，昂贵的，并将，总的来说，只感兴趣的专家在数论。
NIVEN, IVAN, Diophantine Approximations (Interscience Tracts in Pure and Applied Mathematics, No. 14, John Wiley & Sons, New York), viii+68 pp., 36s. This small attractive book arose out of a course of lectures delivered by the author at the 1960 summer meeting of the Mathematical Association of America. It gives proofs of basic results on homogeneous and non-homogeneous approximation of real and complex numbers, the real case being considered in Chapters 1 and 2 and the complex analogue in Chapters 4 and 5. The remaining chapter contains mainly standard results on the fractional and integral parts of the sequence of multiples of a real number, many of these being concerned with uniform distribution. The proofs given avoid completely the use of continued fractions; many of them are new and elegant, but, largely because of the difficulty of the subject, not all are as simple as their appearance would suggest. Apart from the inclusion of the usually neglected basic results on approximation in the complex case, the most useful features of the book are the comments and facts contained in the sections entitled " Further results " at the ends of the chapters, and the extensive and up-to-date Bibliography. The book is, for its size, expensive and will, on the whole, be of interest only to the specialist in Number Theory.