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

作者：James Kevin^*; Smith Ethan

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2013, 154(3): 499-525.

DOI：10.1017/S0305004112000631

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 %26quot;on average%26quot; 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.

• 出版日期2013-5