Number theory and polynomials /
Number Theory & Polynomials
[edited by] James McKee, Chris Smyth.
- Cambridge : Cambridge University Press, 2008.
- 1 online resource (xiv, 349 pages) : digital, PDF file(s).
- London Mathematical Society lecture note series ; 352 .
- London Mathematical Society lecture note series ; 352. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
The trace problem for totally positive algebraic integers / Appendix / Mahler's measure: from Number theory to geometry / Explicit calculation of elliptic fibrations of K3-surfaces and their Belyi-maps / The merit factor problem / Barker sequences and flat polynomials / The Hansen-Mullen primitivity conjecture: completion of proof / An inequality for the multiplicity of the roots of a polynomial / Newman's inequality for in creasing exponential sums / On primitive divisors of nē + b / Julian Aguirre and Juan Carlos Peral ; Jean-Pierre Serre -- Marie Jose Bertin -- Frits Beukers and Hans Montanus -- Peter Borwein, Ron Ferguson and Joshua Knauer -- Peter Borwein and Michael Mossinghoff -- Stephen Cohen and Mateja Presern -- Arturas Dubickas -- Tamas Erdelyi -- Graham Everest and Glyn Harman. Irreducibility and greatest common divisor algorithms for sparse polynomials / Consequences of the continuity of the monic integer transfinite diameter / Nonlinear recurrence sequences and Laurent polynomials / Conjugate algebraic numbers on conics : a survey / On polynomial ergodic averages and square functions / Polynomial inequalities, Mahler's measure, and multipliers / Integer transfinite diameter and computation of polynomials / Smooth divisors of polynomials / Self-inversive polynomials with all zeros on the unit circle / The Mahler measure of algebraic numbers: a survey / Michael Filaseta, Andrew Granville and Andrzej Schinzel -- Jan Hilmar -- Andrew Hone -- James McKee -- Radhakrishnan Nair -- Igor E. Pritsket -- Georges Rhin and Qiang Wu -- Eira Scourfield -- Christopher Sinclair and Jeffrey Vaaler -- Chris Smyth.
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.
9780511721274 (ebook)
Number theory--Congresses. Polynomials--Congresses.