Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Trigonometric polynomials with many real zeros and a Littlewood-type problem


Authors: Peter Borwein and Tamás Erdélyi
Journal: Proc. Amer. Math. Soc. 129 (2001), 725-730
MSC (2000): Primary 41A17
Published electronically: November 3, 2000
MathSciNet review: 1801998
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We examine the size of a real trigonometric polynomial of degree at most $n$ having at least $k$ zeros in $K := {\mathbb{R}} (\text{mod} 2\pi )$ (counting multiplicities). This result is then used to give a new proof of a theorem of Littlewood concerning flatness of unimodular trigonometric polynomials. Our proof is shorter and simpler than Littlewood's. Moreover our constant is explicit in contrast to Littlewood's approach, which is indirect.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 41A17

Retrieve articles in all journals with MSC (2000): 41A17


Additional Information

Peter Borwein
Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: pborwein@cecm.sfu.ca

Tamás Erdélyi
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: terdelyi@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-06021-4
PII: S 0002-9939(00)06021-4
Keywords: Real trigonometric polynomials, real zeros, unimodular trigonometric polynomials, flatness
Received by editor(s): March 2, 1999
Published electronically: November 3, 2000
Additional Notes: The research of the first author was supported, in part, by NSERC of Canada. The research of the second author was supported, in part, by the NSF under Grant No. DMS–9623156.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 Copyright retained by the authors