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2 results

  • Integral points of bounded degree on affine curves

  • Part of
  • Aaron Levin
  • Journal:
    Compositio Mathematica / Volume 152 / Issue 4 / April 2016
    Published online by Cambridge University Press:
    26 November 2015, pp. 754-768
    Print publication:
    April 2016
    • Article
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  • We generalize Siegel’s theorem on integral points on affine curves to integral points of bounded degree, giving a complete characterization of affine curves with infinitely many integral points of degree $d$ or less over some number field. Generalizing Picard’s theorem, we prove an analogous result characterizing complex affine curves admitting a nonconstant holomorphic map from a degree $d$ (or less) analytic cover of $\mathbb{C}$.

  • 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

  • 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 $\alpha$.