Average frobenius distribution for the degree two primes of a number field
Document Type
Article
Publication Date
5-1-2013
Abstract
Let K be a number field and r an integer. Given an elliptic curve E, defined over K, we consider the problem of counting the number of degree two prime ideals of K with trace of Frobenius equal to r. Under certain restrictions on K, we show that on average the number of such prime ideals with norm less than or equal to x 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. © Cambridge Philosophical Society 2013.
Publication Title
Mathematical Proceedings of the Cambridge Philosophical Society
Recommended Citation
James, K.,
&
Smith, E.
(2013).
Average frobenius distribution for the degree two primes of a number field.
Mathematical Proceedings of the Cambridge Philosophical Society,
154(3), 499-525.
http://doi.org/10.1017/S0305004112000631
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/7757