2022/01/19 by Robin Visser, Visser, Robin
Computer Science · Social Sciences · #11G30 #Cryptography and Residue Arithmetic #FOS: Mathematics #Historical Geopolitical and Social Dynamics #Historical and Political Studies #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2201.07825
openalex publication_date 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a number field, and g ≥ 2 a positive integer. We define cK(g) as the smallest integer n such that there exist infinitely many K-isomorphism classes of genus g hyperelliptic curves C/K with all Weierstrass points in K having potentially good reduction outside n primes in K. We show that cK(g) > π_K, \textrmodd(2g) + 1, where π_K, \textrmodd(n) denotes the number of odd primes in K with norm no greater than n, as well as present a summary of various conditional and unconditional results on upper bounds for cK(g).