ON FIXED POINTS OF DOUBLY SYMMETRIC RIEMANN SURFACES
2008 ◽
Vol 50
(3)
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pp. 371-378
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AbstractIn this paper, we study ovals of symmetries and the fixed points of their products on Riemann surfaces of genus g ≥ 2. We show how the number of these points affects the total number of ovals of symmetries. We give a generalisation of Bujalance, Costa and Singerman's theorems in which we show upper bounds for the total number of ovals of two symmetries in terms of g, the order n and the number m of the fixed points of their product, and we show their attainments for n holding some divisibility conditions. Finally, we give an upper bound for m in terms of n and g, and we study conditions under which it has given parity.
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1993 ◽
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pp. 221-249
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1996 ◽
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pp. 335-370
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2012 ◽
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1970 ◽
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pp. 922-932
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2016 ◽
Vol 30
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pp. 622-639
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