Abstract
The Littlewood problem concerns the size of the L p norm on the boundary of D of Littlewood polynomials. When p > 2 it asks how small the L p norm can be, and when p 〈 2 it asks how large the L p norm can be. In both cases we are interested in how close these norms can be to the L2 norm. Recall that the L 2 norm of a Littlewood polynomial of degree n is \( \sqrt {{n + 1}} \) That the behaviour changes at p = 2 is expected from Hölder’s inequality, which gives, for 1 ≤ α 〈 β ≤ 00 and α -1 + β -1 = 1, that
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© 2002 Springer-Verlag New York, Inc.
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Borwein, P. (2002). The Littlewood Problem. In: Computational Excursions in Analysis and Number Theory. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21652-2_15
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DOI: https://doi.org/10.1007/978-0-387-21652-2_15
Publisher Name: Springer, New York, NY
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