IJPAM: Volume 45, No. 4 (2008)
THE BRUGGEMAN-KUZNETSOV TRACE FORMULAS II
P.O. Box 1424, Princeton, NJ 08542, USA
e-mail: cjm@ix.netcom.com
Abstract.Determining the -level correlation of the eigenvalues of
the hyperbolic Laplacian for the modular surface is a
notoriously difficult problem, and very little of substance
is known.
In Part I we showed that with regard to one aspect of this problem one gets a dramatically better result by the Bruggeman-Kuznetsov trace formula. In this Part II we show that with regard to another aspect of the problem one gets a dramatically better result by the Selberg trace formula.
In this paper, in addition to the Selberg trace formula, we
employ the Rudnick-Sarnak construction, which
was created to analyze the -level correlation of the zeros
of the Riemann zeta function and principal
-functions,
together with the weighted Bruggeman-Kuznetsov trace formula,
as formulated by Sarnak and Iwaniec.
Received: April 21, 2008
AMS Subject Classification: 11F03, 11F11, 11F12, 11F72
Key Words and Phrases: modular group, pair correlation, eigenvalues, Laplacian, Selberg trace formula, Bruggeman-Kuznetsov trace formula
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 45
Issue: 4