Number Theory and Polynomials

Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.

James McKee (Edited by), Chris Smyth (Edited by)

9780521714679, Cambridge University Press

Paperback, published 8 May 2008

364 pages, 16 b/w illus. 4 colour illus. 26 tables
22.8 x 15 x 1.9 cm, 0.51 kg

'… certainly interesting not only for those interested in some selected topic but also for those who like to browse the papers with the aim of extending their knowledge.' EMS Newsletter

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.

Preface
Index of authors
List of participants
Conference photograph, with key
The trace problem for totally positive algebraic integers Julián Aguirre and Juan Carlos Peral, with an appendix by Jean-Pierre Serre
Mahler's measure: from Number Theory to Geometry Marie José 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 Prešern
An inequality for the multiplicity of the roots of a polynomial Art?ras Dubickas
Newman's inequality for increasing exponential sums Tamás Erdélyi
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. Pritsker
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.

Subject Areas: Number theory [PBH]