JournalsrmiVol. 16, No. 3pp. 515–527

On ovals on Riemann surfaces

  • Grzegorz Gromadzki

    University of Gdańsk, Poland
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We prove that k(k9)k (k ≥ 9) non-conjugate symmetries of a Riemann surface of genus gg have at most 2g2+2r3(9k)2g-2+2^{r-3}(9-k) ovals in total, where rr is the smallest positive integer for which k2r1k≤2^{r-1}. Furthermore we prove that for arbitrary k9k≥9 this bound is sharp for infinitely many values of gg.

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Grzegorz Gromadzki, On ovals on Riemann surfaces. Rev. Mat. Iberoam. 16 (2000), no. 3, pp. 515–527

DOI 10.4171/RMI/282