Journal of the Mathematical Society of Japan

Limit formulas of period integrals for a certain symmetric pair II

Masao TSUZUKI

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Abstract

Let $(G,H) = (U(p,q),U(p-1,q) \times U(1))$ and $\{\Gamma_n\}$ a tower of congruence uniform lattices in $G$. By the period integrals of automorphic forms on $\Gamma \backslash G$ along $\Gamma_n \cap H\backslash H$ , we introduce a certain discrete measure $d \mu^H_{\Gamma_n}$ on the $H$-spherical unitary dual of $G$. It is shown that the sequence of measures $d \mu^H_{\Gamma_n}$ with growing $n$ converges in a weak sense to the Plancherel measure $d \mu^H$ for the symmetric space $H\backslash G$.

Article information

Source
J. Math. Soc. Japan Volume 63, Number 3 (2011), 1039-1084.

Dates
First available: 1 August 2011

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1312203811

Digital Object Identifier
doi:10.2969/jmsj/06331039

Zentralblatt MATH identifier
05950732

Mathematical Reviews number (MathSciNet)
MR2836755

Subjects
Primary: 11F72: Spectral theory; Selberg trace formula
Secondary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 11F36

Keywords
periods of automorphic forms Plancherel measures relative trace formulas

Citation

TSUZUKI, Masao. Limit formulas of period integrals for a certain symmetric pair II. Journal of the Mathematical Society of Japan 63 (2011), no. 3, 1039--1084. doi:10.2969/jmsj/06331039. http://projecteuclid.org/euclid.jmsj/1312203811.


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