Geodesic
A Remark on a Modular Analogue of the Sato–Tate Conjecture
Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 234-242

Voir la notice de l'article provenant de la source Cambridge University Press

The original Sato–Tate Conjecture concerns the angle distribution of the eigenvalues arising from non-CM elliptic curves. In this paper, we formulate amodular analogue of the Sato–Tate Conjecture and prove that the angles arising from non- $\text{CM}$ holomorphic Hecke eigenforms with non-trivial central characters are not distributed with respect to the Sate–Tatemeasure for non- $\text{CM}$ elliptic curves. Furthermore, under a reasonable conjecture, we prove that the expected distribution is uniform.
DOI : 10.4153/CMB-2007-025-7
Mots-clés : 11F03, 11F25, L-functions, Elliptic curves, Sato–Tate 
Kuo, Wentang. A Remark on a Modular Analogue of the Sato–Tate Conjecture. Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 234-242. doi: 10.4153/CMB-2007-025-7
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