Number Theory and Polynomials

Klappentext Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory. Zusammenfassung Containing the latest research! this volume is essential for readers looking for a snapshot of current progress in polynomials and number theory. Contributions by leading experts in the field include recent work on the Schur-Siegel-Smyth trace problem! Mahler measure! the merit factor problem! Barker sequences! and K3-surfaces. Inhaltsverzeichnis 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....

Autorentext
James McKee is a Senior Lecturer in the Department of Mathematics at Royal Holloway, University of London. Chris Smyth is a Reader in the School of Mathematics and the Maxwell Institute for Mathematical Sciences at the University of Edinburgh.

Zusammenfassung
Containing the latest research, this volume is essential for readers looking for a snapshot of current progress in polynomials and number theory. Contributions by leading experts in the field include recent work on the Schur-Siegel-Smyth trace problem, Mahler measure, the merit factor problem, Barker sequences, and K3-surfaces.

Inhalt
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.

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