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on littlewood's constants

  • d. beliaev (a1) and s. smirnov (a2)
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 $\alpha$.

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the authors would like to thank the göran gustafsson foundation for its generous support.
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Bulletin of the London Mathematical Society
  • ISSN: 0024-6093
  • EISSN: 1469-2120
  • URL: /core/journals/bulletin-of-the-london-mathematical-society
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