On totally split primes in high-degree torsion fields of elliptic curves

2020/09/28 by Merikoski, Jori
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2009.13119

Abstract

Analogously to primes in arithmetic progressions to large moduli, we can study primes that are totally split in extensions of ℚ of high degree. Motivated by a question of Kowalski we focus on the extensions ℚ(E[d]) obtained by adjoining the coordinates of d-torsion points of a non-CM elliptic curve E/ℚ. A prime p is said to be an outside prime of E if it is totally split in ℚ(E[d]) for some d with p

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