JournalsrmiVol. 16, No. 3pp. 515–527

On ovals on Riemann surfaces

  • Grzegorz Gromadzki

    University of Gdańsk, Poland
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Abstract

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.

Cite this article

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

DOI 10.4171/RMI/282