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arXiv · 2009.02485

Splitting of primes in number fields generated by points on some modular curves

Filip Najman·Antonela Trbović
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Abstract

We study the splitting of primes in number fields generated by points on modular curves. Momose was the first to notice that quadratic points on $X_1(n)$ generate quadratic fields over which certain primes split in a particular way and his results were later expanded upon by Krumm. We prove results about the splitting behaviour of primes in quadratic fields generated by points on the modular curves $X_0(n)$ which are hyperelliptic (except for $n=37$) and in cubic fields generated by points on $X_1(2, 14)$.

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Filip Najman, Antonela Trbović. 2022-01-25. Splitting of primes in number fields generated by points on some modular curves. https://arxiv.org/abs/2009.02485

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