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

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

2011-09-19

arxiv.org/abs/1109.4007v1

Mathematics

Number Theory

Scientific paper

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.

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