| 书目名称 | Computational Excursions in Analysis and Number Theory |
| 编辑 | Peter Borwein |
| 视频video | |
| 丛书名称 | CMS Books in Mathematics |
| 图书封面 |  |
| 描述 | This book is designed for a topics course in computational number theory. It is based around a number of difficult old problems that live at the interface of analysis and number theory. Some of these problems are the following: The Integer Chebyshev Problem. Find a nonzero polynomial of degree n with integer eoeffieients that has smallest possible supremum norm on the unit interval. Littlewood‘s Problem. Find a polynomial of degree n with eoeffieients in the set { + 1, -I} that has smallest possible supremum norm on the unit disko The Prouhet-Tarry-Escott Problem. Find a polynomial with integer co effieients that is divisible by (z - l)n and has smallest possible 1 norm. (That 1 is, the sum of the absolute values of the eoeffieients is minimal.) Lehmer‘s Problem. Show that any monie polynomial p, p(O) i- 0, with in teger coefficients that is irreducible and that is not a cyclotomic polynomial has Mahler measure at least 1.1762 .... All of the above problems are at least forty years old; all are presumably very hard, certainly none are completely solved; and alllend themselves to extensive computational explorations. The techniques for tackling these problems are various and inclu |
| 出版日期 | Book 2002 |
| 关键词 | Diophantine approximation; Maxima; algorithms; calculus; combinatorics; computational number theory; extre |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-0-387-21652-2 |
| isbn_softcover | 978-1-4419-3000-2 |
| isbn_ebook | 978-0-387-21652-2Series ISSN 1613-5237 Series E-ISSN 2197-4152 |
| issn_series | 1613-5237 |
| copyright | Springer Science+Business Media New York 2002 |
发表于 2025-3-21 17:26:17
