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Number Theory and Polynomials

Number Theory and Polynomials

£52.00

Part of London Mathematical Society Lecture Note Series

Julián Aguirre, Juan Carlos Peral, Jean-Pierre Serre, Marie José Bertin, Frits Beukers, Hans Montanus, Peter Borwein, Ron Ferguson, Joshua Knauer, Michael Mossinghoff, Stephen Cohen, Mateja Prešern, Artūras Dubickas, Tamás Erdélyi, Graham Everest, Glyn Harman, Michael Filaseta, Andrew Granville, Andrzej Schinzel, Jan Hilmar, Andrew Hone, James McKee, Radhakrishnan Nair, Igor E. Pritsker, Georges Rhin, Qiang Wu, Eira Scourfield, Christopher Sinclair, Jeffrey Vaaler, Chris Smyth
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  • Date Published: May 2008
  • availability: In stock
  • format: Paperback
  • isbn: 9780521714679

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  • 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.

    • 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
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    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

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    Product details

    • Date Published: May 2008
    • format: Paperback
    • isbn: 9780521714679
    • length: 364 pages
    • dimensions: 228 x 150 x 19 mm
    • weight: 0.51kg
    • contains: 16 b/w illus. 4 colour illus. 26 tables
    • availability: In stock
  • 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.

  • Editors

    James McKee, Royal Holloway, University of London
    James McKee is a Senior Lecturer in the Department of Mathematics at Royal Holloway, University of London.

    Chris Smyth, University of Edinburgh
    Chris Smyth is a Reader in the School of Mathematics and the Maxwell Institute for Mathematical Sciences at the University of Edinburgh.

    Contributors

    Julián Aguirre, Juan Carlos Peral, Jean-Pierre Serre, Marie José Bertin, Frits Beukers, Hans Montanus, Peter Borwein, Ron Ferguson, Joshua Knauer, Michael Mossinghoff, Stephen Cohen, Mateja Prešern, Artūras Dubickas, Tamás Erdélyi, Graham Everest, Glyn Harman, Michael Filaseta, Andrew Granville, Andrzej Schinzel, Jan Hilmar, Andrew Hone, James McKee, Radhakrishnan Nair, Igor E. Pritsker, Georges Rhin, Qiang Wu, Eira Scourfield, Christopher Sinclair, Jeffrey Vaaler, Chris Smyth

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