Number variance for SL(2,Z)\H
نویسندگان
چکیده
We examine the variance of the number of eigenvalues of the Laplacian for the modular surface in a short interval. The analysis allows for the interval to be small enough so that the size of the variance is Poissonian. The starting point for the investigation is the Kuznetsov formula and the body of the work consists of studying the complicated off-diagonal contributions which are responsible for the shape of the final asymptotics. A consequence of the main result is a slight improvement of the known lower bound for the remainder term in the Weyl counting function.
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تاریخ انتشار 2004