Number theory and polynomials
著者
書誌事項
Number theory and polynomials
（London Mathematical Society lecture note series, 352）
Cambridge University Press, 2008
- : pbk
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注記
"This volume is the proceedings of a workshop on 'Number Theory and Polynomials' held at Bristol University, 3-7 April 2006."--P. vii
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
- Preface
- Index of authors
- List of participants
- Conference photograph, with key
- The trace problem for totally positive algebraic integers Julian Aguirre and Juan Carlos Peral, with an appendix by Jean-Pierre Serre
- Mahler's measure: from Number Theory to Geometry Marie Jose 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 Presern
- An inequality for the multiplicity of the roots of a polynomial Arturas Dubickas
- Newman's inequality for increasing exponential sums Tamas Erdelyi
- 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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