✦ LIBER ✦

Equidistribution of Hecke eigenforms on the Hilbert modular varieties

✍ Scribed by Sheng-Chi Liu

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 132 KB
Volume: 127
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2007.01.006

No coin nor oath required. For personal study only.

✦ Synopsis

Let F be a totally real number field with ring of integers O, and let Γ = SL(2, O) be the Hilbert modular group. Given the orthonormal basis of Hecke eigenforms in S 2k (Γ ), one can associate a probability measure dμ k on the Hilbert modular variety Γ \H n . We prove that dμ k tends to the invariant measure on Γ \H n weakly as k → ∞. This generalizes Luo's result [W. Luo, Equidistribution of Hecke eigenforms on the modular surface, Proc. Amer. Math. Soc. 131 (2003) 21-27] for the case F = Q.

📜 SIMILAR VOLUMES

Equidistribution of Hecke Eigenforms on

Equidistribution of Hecke Eigenforms on the Arithmetic Surface Γ0(N)H

✍ Yuk-Kam Lau 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 158 KB

Given the orthonormal basis of Hecke eigenforms in S 2k ðGð1ÞÞ; Luo established an associated probability measure dm k on the modular surface Gð1Þ=H that tends weakly to the invariant measure on Gð1Þ=H: We generalize his result to the arithmetic surface G 0 ðNÞ=H where N51 is square-free.

On the Blocks of Modular Hecke Algebras

✍ A.A. Khammash 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 275 KB

On the representation theory of modular

On the representation theory of modular Hecke algebras

✍ Peter Sin 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 545 KB

Conjectures on the fundamental domain of

Conjectures on the fundamental domain of the Hilbert modular group

✍ Jesse Ira Deutsch 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 802 KB

A Remark on the Modularity of Abelian Va

A Remark on the Modularity of Abelian Varieties of GL2-type over Q

✍ Naoki Murabayashi 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 128 KB

Let A be an abelian variety of GL 2 -type over the rational number field Q, without complex multiplication. In this paper, we will show that a modularity of A over the complex number field C implies that of A over Q.