2020/09/05 by Filip Najman, Najman, Filip, Antonela Trbović +1
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.2009.02485
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 X1(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 X0(n) which are hyperelliptic (except for n=37) and in cubic fields generated by points on X1(2, 14).