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Low-degree points on Hurwitz-Klein curves. (English) Zbl 1116.14017
Summary: We investigate low-degree points on the Fermat curve of degree 13, the Snyder quintic curve and the Klein quartic curve. We compute all quadratic points on these curves and use R. F. Coleman ’s effective Chabauty method [Duke Math. J. 52, 765–770 (1985; Zbl 0588.14015)] to obtain bounds for the number of cubic points on each of the former two curves.

MSC:
 14H25 Arithmetic ground fields for curves 11G30 Curves of arbitrary genus or genus $$\ne 1$$ over global fields 14G05 Rational points
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