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Authors
Affiliations
1 Department of Mathematics and Statistics, Concordia University, 1455 De Maisonneuve West Montreal, Quebec H3G 1M8, CA
2 Dipartimento Di Matematica, Universita Roma Tre, Largo S. L. Murialdo, 1, Iβ00191 Rome, IT
Source
Journal of the Ramanujan Mathematical Society, Vol 19, No 3 (2004), Pagination: 181-201
Abstract
Given an integer r, we consider the problem of enumerating the inert prime ideals π of β(i) for which a given elliptic curve E has trace of Frobenius atΒ π equal to r. We prove that on average the number of such prime ideals up to x is asymptotic to cr log log x where cr is an explicit constant computed in terms of an Euler product. This result is in accordance with the standard heuristics. This problem generalises naturally the classical Lang-Trotter conjecture for elliptic curves over β.