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- Title
Splitting of primes in number fields generated by points on some modular curves.
- Authors
Najman, Filip; Trbović, Antonela
- Abstract
We study the splitting of primes in number fields generated by points on modular curves. Momose (Nagoya Math J 96:139–165, 1984) 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 (Quadratic Points on Modular Curves. PhD thesis, University of Georgia, 2013). 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) .
- Subjects
UNIVERSITY of Georgia; QUADRATIC fields; PRIME numbers; QUADRATIC equations; MATHEMATICS
- Publication
Research in Number Theory, 2022, Vol 8, Issue 2, p1
- ISSN
2522-0160
- Publication type
Article
- DOI
10.1007/s40993-022-00325-w