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Bulletin of the London Mathematical Society (1)

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1 results

on littlewood's constants
d. beliaev, s. smirnov
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 5 / October 2005

Published online by Cambridge University Press:

23 September 2005, pp. 719-726

Print publication:

October 2005
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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 $\alpha$.