ErgodicPNT

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

Piatetski-Shapiro Primes

This earlier problem is of considerable importance in algorithmic number theory, and both have been excellent testing and breeding grounds for various important techniques, notably (and this is close to my heart…) leading to the invention and development of the first “large sieve” method by Linnik.