The average norm of polynomials of fixed height

Authors:
Peter Borwein and Kwok-Kwong Stephen Choi

Journal:
Trans. Amer. Math. Soc. **359** (2007), 923-936

MSC (2000):
Primary 11C08, 26C05

Published electronically:
September 12, 2006

MathSciNet review:
2255202

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be any integer and let

In this paper we give exact formulae for for various values of . We also give a variety of related results for different classes of polynomials including polynomials of fixed height H, polynomials with coefficients and reciprocal polynomials. The results are surprisingly precise. Typical of the results we get is the following.

**Theorem 0.1.** *For , we have *

*and*

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Additional Information

**Peter Borwein**

Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Email:
pborwein@cecm.sfu.ca

**Kwok-Kwong Stephen Choi**

Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Email:
kkchoi@cecm.sfu.ca

DOI:
http://dx.doi.org/10.1090/S0002-9947-06-03952-3

Keywords:
Polynomials of height 1,
Littlewood polynomials,
average $L_p$ norm

Received by editor(s):
June 19, 2001

Received by editor(s) in revised form:
January 22, 2005

Published electronically:
September 12, 2006

Additional Notes:
The research of the first author was supported by MITACS and by NSERC of Canada, and the research of the second author was supported by NSERC of Canada.

Article copyright:
© Copyright 2006
by the authors