Number Theory and Polynomials (eBook, PDF)

Redaktion: Mckee, James

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 8. Mai 2008
• Englisch
• ISBN-13: 9780511894121
• Artikelnr.: 38194540

Inhaltsangabe

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
Preern; 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.