数域二次素理想的平均Frobenius分布
数论
2013-07-08 v2
摘要
设 be a number field and an integer. Given an elliptic curve , defined over , we consider the problem of counting the number of degree two prime ideals of with trace of Frobenius equal to . Under certain restrictions on , we show that "on average" the number of such prime ideals with norm less than or equal to satisfies an asymptotic identity that is in accordance with standard heuristics. This work is related to the classical Lang-Trotter conjecture and extends the work of several authors.
引用
@article{arxiv.1109.4007,
title = {Average Frobenius distribution for the degree two primes of a number field},
author = {Kevin James and Ethan Smith},
journal= {arXiv preprint arXiv:1109.4007},
year = {2013}
}