Number theory and polynomials / [edited by] James McKee, Chris Smyth.

Format:

Book

Contributor:

McKee, James (James Fraser), editor.

Smyth, Chris, editor.

Series:

London Mathematical Society lecture note series ; 352.

London Mathematical Society lecture note series ; 352

Language:

English

Subjects (All):

Number theory--Congresses.

Number theory.

Polynomials--Congresses.

Polynomials.

Physical Description:

1 online resource (xiv, 349 pages) : digital, PDF file(s).

Other Title:

Number Theory & Polynomials

Place of Publication:

Cambridge : Cambridge University Press, 2008.

Language Note:

English

Summary:

Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol drew together international researchers with a variety of number-theoretic interests, and the book's contents reflect the quality of the meeting. Topics covered include recent work on the Schur-Siegel-Smyth trace problem, Mahler measure and its generalisations, the merit factor problem, Barker sequences, K3-surfaces, self-inversive polynomials, Newman's inequality, algorithms for sparse polynomials, the integer transfinite diameter, divisors of polynomials, non-linear recurrence sequences, polynomial ergodic averages, and the Hansen-Mullen primitivity conjecture. With surveys and expository articles presenting the latest research, this volume is essential for graduates and researchers looking for a snapshot of current progress in polynomials and number theory.

Contents:

The trace problem for totally positive algebraic integers / Julian Aguirre and Juan Carlos Peral ; Appendix / Jean-Pierre Serre

Mahler's measure: from Number theory to geometry / Marie Jose Bertin

Explicit calculation of elliptic fibrations of K3-surfaces and their Belyi-maps / Frits Beukers and Hans Montanus

The merit factor problem / Peter Borwein, Ron Ferguson and Joshua Knauer

Barker sequences and flat polynomials / Peter Borwein and Michael Mossinghoff

The Hansen-Mullen primitivity conjecture: completion of proof / Stephen Cohen and Mateja Presern

An inequality for the multiplicity of the roots of a polynomial / Arturas Dubickas

Newman's inequality for in creasing exponential sums / Tamas Erdelyi

On primitive divisors of n² + b / Graham Everest and Glyn Harman.

Irreducibility and greatest common divisor algorithms for sparse polynomials / Michael Filaseta, Andrew Granville and Andrzej Schinzel

Consequences of the continuity of the monic integer transfinite diameter / Jan Hilmar

Nonlinear recurrence sequences and Laurent polynomials / Andrew Hone

Conjugate algebraic numbers on conics : a survey / James McKee

On polynomial ergodic averages and square functions / Radhakrishnan Nair

Polynomial inequalities, Mahler's measure, and multipliers / Igor E. Pritsket

Integer transfinite diameter and computation of polynomials / Georges Rhin and Qiang Wu

Smooth divisors of polynomials / Eira Scourfield

Self-inversive polynomials with all zeros on the unit circle / Christopher Sinclair and Jeffrey Vaaler

The Mahler measure of algebraic numbers: a survey / Chris Smyth.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-139-88273-2

1-107-36793-X

1-107-37246-1

1-107-36302-0

1-107-36890-1

1-299-40552-5

1-107-36547-3

0-511-89412-0

0-511-72127-7