Rational functions on algebraic curves, which have a single zero and a single pole, are considered. A pair consisting of such a function and a curve is called an Abel pair; a special case of an Abel pair is a Belyi pair. In the present paper, moduli spaces of Abel pairs for curves of genus one are studied. In particular, a number of Belyi pairs over the fields ℂ and \( \overline{{\mathbb{F}}_p} \) is computed. This approach could be fruitfully used in studying Hurwitz spaces and modular curves for fields of finite characteristics.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 446, 2016, pp. 165–181.
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Oganesyan, D. Abel Pairs and Modular Curves. J Math Sci 226, 655–666 (2017). https://doi.org/10.1007/s10958-017-3556-4
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DOI: https://doi.org/10.1007/s10958-017-3556-4