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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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Barker sequences and flat polynomials
by
Michael Mossinghoff
Davidson College
Coauthors: Peter Borwein (Simon Fraser University), Erich Kaltofen (North Carolina State University)

A Barker sequence is a finite sequence of integers a0, ..., an-1, each ±1, for which |∑j aj aj+k| ≤ 1 for k ≠ 0. It has long been conjectured that no Barker sequences exist with length n > 13. We describe some recent work connecting this problem to several open questions posed by Littlewood, Mahler, Erdös, Newman, Golay, and others about the existence of polynomials with ±1 coefficients that are "flat" in some sense over the unit circle. We will also briefly describe some recent related work concerning Lp norms and Mahler's measure of polynomials.

Date received: June 15, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxo-06.