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on littlewood's constants

Published online by Cambridge University Press:  23 September 2005

d. beliaev  and
s. smirnov
d. beliaev
Affiliation:
kungliga tekniska högskolan, inst. för matematik, 100 44 stockholm, swedenbeliaev@math.kth.se, stas@math.kth.se
s. smirnov
Affiliation:
université de genève, section de mathématiques, 2-4, rue du lièvre, case postale 240, 1211 genève 24, switzerlandstanislav.smirnov@math.unige.ch
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Abstract

in two papers, littlewood studied seemingly unrelated constants: (i) the best $\alpha$ such that for any polynomial $f$, of degree $n$, the areal integral of its spherical derivative is at most $\const\cdot n^\alpha$, and (ii) the extremal growth rate $\beta$ of the length of green's equipotentials for simply connected domains. these two constants are shown to coincide, thus greatly improving known estimates on $\alpha$.

Keywords

30c50 (primary)30c8530d35 (secondary)
Type
papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 5 , October 2005 , pp. 719 - 726
Copyright
the london mathematical society 2005

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Footnotes

the authors would like to thank the göran gustafsson foundation for its generous support.