Preface Introduction LLL and PSLQ Pisot and Salem Numbers Rudin-Shapiro Polynomials Fekete Polynomials Products of Cyclotomic Polynomials Location of Zeros Maximal Vanishing Diophantine Approximation of Zeros The Integer-Chebyshev Problem The Prouhet-Tarry-Escott Problem The Easier Waring Problem The Erdös-Szekeres Problem Barker Polynomials and Golay Pairs The Littlewood Problem Spectra Appendix A: A Compendium of Inequalities B: Lattice Basis Reduction and Integer Relations C: Explicit Merit Factor Formulae D: Research Problems References Index
* Preface * Introduction * LLL and PSLQ * Pisot and Salem Numbers * Rudin-Shapiro Polynomials * Fekete Polynomials * Products of Cyclotomic Polynomials * Location of Zeros * Maximal Vanishing * Diophantine Approximation of Zeros * The Integer-Chebyshev Problem * The Prouhet-Tarry-Escott Problem * The Easier Waring Problem * The Erdös-Szekeres Problem * Barker Polynomials and Golay Pairs * The Littlewood Problem * Spectra * Appendix A: A Compendium of Inequalities * B: Lattice Basis Reduction and Integer Relations * C: Explicit Merit Factor Formulae * D: Research Problems * References * Index
This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.
This book is designed for a course in computational number theory. It is based around a number of difficult old problems that live at the interface of analytic, computational and Diophantine number theory. The techniques for tackling these problems are various and include probabilistic methods, combinatorial methods, Diophantine and analytic techniques. The main computational tool used is the LLL algorithm for finding small vectors in a lattice. The book is intended as an introduction to a diverse collection of techniques for solving number- theoretic problems. For all chapters, the author has suggested related research papers where additional details may be pursued. There are many exercises and open research problems included. Indeed