1. CMB 2007 (vol 50 pp. 234)
|A Remark on a Modular Analogue of the Sato--Tate Conjecture |
The original Sato--Tate Conjecture concerns the angle distribution of the eigenvalues arising from non-CM elliptic curves. In this paper, we formulate a modular analogue of the Sato--Tate Conjecture and prove that the angles arising from non-CM holomorphic Hecke eigenforms with non-trivial central characters are not distributed with respect to the Sate--Tate measure for non-CM elliptic curves. Furthermore, under a reasonable conjecture, we prove that the expected distribution is uniform.
Keywords:$L$-functions, Elliptic curves, Sato--Tate