#### Title

Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals

#### Document Type

Article

#### Publication Date

5-1-2011

#### Abstract

Copyright © Cambridge Philosophical Society 2011. Let K be a fixed number field, assumed to be Galois over Q. Let r and f be fixed integers with f positive. Given an elliptic curve E, defined over K, we consider the problem of counting the number of degree f prime ideals of K with trace of Frobenius equal to r. Except in the case f = 2, 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.

#### Publication Title

Mathematical Proceedings of the Cambridge Philosophical Society

#### Recommended Citation

James, K.,
&
Smith, E.
(2011).
Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals.
*
Mathematical Proceedings of the Cambridge Philosophical Society,
150*(3), 439-458.
http://doi.org/10.1017/S0305004111000041

Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/7756