Isbn: 9780387954448 - computational excursions in analysis and number theory (15 risultati)

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Condizione: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | 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 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.…

Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included. 236 pp. Englisch.…

Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic proble.…

Buch. Condizione: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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 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.…

Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book is designed for a course in computational number theory. It is based around a number of difficult old problems that live at the interface of analytic, computational and Diophantine number theory. The techniques for tackling these problems are various and include probabilistic methods, combinatorial methods, Diophantine and analytic techniques. The main computational tool used is the LLL algorithm for finding small vectors in a lattice. The book is intended as an introduction to a diverse collection of techniques for solving number- theoretic problems. For all chapters, the author has suggested related research papers where additional details may be pursued. There are many exercises and open research problems included. IndeedSpringer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 236 pp. Englisch.…