A Remark on a Modular Analogue of the Sato¿Tate Conjecture

• Autores: Wentang Kuo
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 2, 2007, págs. 234-242
• Idioma: inglés
• DOI: 10.4153/cmb-2007-025-7
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• Resumen

  • 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.