{"product_id":"9780387954448","title":"CMS Books in Mathematics","description":"\u003ch1\u003eCMS Books in Mathematics\u003c\/h1\u003e \u003ch2\u003eBorwein, Peter\u003c\/h2\u003e \u003cp\u003eThis 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 include proba­ bilistic methods, combinatorial methods, \"the circle method,\" and Diophantine and analytic techniques. Computationally, the main tool is the LLL algorithm for finding small vectors in a lattice. The book is intended as an introduction to a diverse collection of techniques.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2002-07-12\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387954448\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-0-387-21652-2\u003c\/p\u003e \u003cp\u003eDimensions: cm xcm\u003c\/p\u003e \u003cp\u003ePages: 220\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":46541655474316,"sku":"9780387954448","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387954448.jpg?v=1775744608","url":"https:\/\/lateknightbooks.com\/products\/9780387954448","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}