Average frobenius distribution for the degree two primes of a number field

Document Type


Publication Date



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