On a conjecture of H. Rauch on theta constants and Riemann surfaces with many automorphisms.
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H. Popp (1972)
Journal für die reine und angewandte Mathematik
R. O. Buchweitz (1976/1977)
Séminaire sur les singularités des surfaces
Arnaldo Garcia (1993)
Manuscripta mathematica
Grzegorz Gromadzki (2000)
Revista Matemática Iberoamericana
We prove that k (k ≥ 9) non-conjugate symmetries of a Riemann surface of genus g have at most 2g - 2 + 2r - 3(9 - k) ovals in total, where r is the smallest positive integer for which k ≤ 2r - 1. Furthermore we prove that for arbitrary k ≥ 9 this bound is sharp for infinitely many values of g.
Notari, R. (1999)
Rendiconti del Seminario Matematico
Costa, Antonio F., Izquierdo, Milagros (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
Jiryo Komeda (1992)
Manuscripta mathematica
Frank Loose (1989)
Manuscripta mathematica
A. Ragusa, G. Paxia, G. Raciti (1992)
Manuscripta mathematica
Karl-Otto Stöhr (1993)
Journal für die reine und angewandte Mathematik
Jesus J. Ortega (1991)
Mathematische Annalen
H.F. Baker (1894)
Mathematische Annalen
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