Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves

Min Sha, and Igor E. Shparlinski. "Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves." Acta Arithmetica 170.4 (2015): 299-325. <http://eudml.org/doc/286601>.

@article{MinSha2015,
abstract = {We obtain new results concerning the Lang-Trotter conjectures on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In particular, we improve a result of A. C. Cojocaru and the second author (2008) towards the Lang-Trotter conjecture on average for polynomially parameterised families of elliptic curves when the parameter runs through a set of rational numbers of bounded height. Some of the families we consider are much thinner than the ones previously studied.},
author = {Min Sha, Igor E. Shparlinski},
journal = {Acta Arithmetica},
keywords = {Lang-Trotter conjecture; Sato-Tate conjecture; parametric families of elliptic curves},
language = {eng},
number = {4},
pages = {299-325},
title = {Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves},
url = {http://eudml.org/doc/286601},
volume = {170},
year = {2015},
}

TY - JOUR
AU - Min Sha
AU - Igor E. Shparlinski
TI - Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves
JO - Acta Arithmetica
PY - 2015
VL - 170
IS - 4
SP - 299
EP - 325
AB - We obtain new results concerning the Lang-Trotter conjectures on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In particular, we improve a result of A. C. Cojocaru and the second author (2008) towards the Lang-Trotter conjecture on average for polynomially parameterised families of elliptic curves when the parameter runs through a set of rational numbers of bounded height. Some of the families we consider are much thinner than the ones previously studied.
LA - eng
KW - Lang-Trotter conjecture; Sato-Tate conjecture; parametric families of elliptic curves
UR - http://eudml.org/doc/286601
ER -