Journal of the Mathematical Society of Japan

Limit formulas of period integrals for a certain symmetric pair II


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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

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

First available: 1 August 2011

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Zentralblatt MATH identifier

Mathematical Reviews number (MathSciNet)

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

periods of automorphic forms Plancherel measures relative trace formulas


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.

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