Number Theory and Polynomials
Number Theory and Polynomials
£67.00
GBPMany 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.
- An invaluable resource to both students and experts in this area, with survey articles on the most important topics in the field
- Expository articles introduce graduate students to some problems of active interest
- The inclusion of new results from leading experts in the field provides a snapshot of current progress
Reviews & endorsements
'… 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
Product details
May 2008Paperback
9780521714679
364 pages
228 × 150 × 19 mm
0.51kg
16 b/w illus. 4 colour illus. 26 tables
Available
Table of Contents
- 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 Artūras 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.
