M ay 2 00 6 A prime geodesic theorem for SL 4
نویسنده
چکیده
1 Euler Characteristics and Infinitesimal Characters 4 1.1 The unitary duals of SL2(R) and SL4(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Euler characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Euler-Poincaré functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Euler characteristics in the case of SL4(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 The unitary dual of KM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 Infinitesimal characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
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Contents Introduction iii 1 Euler Characteristics and Infinitesimal Characters 1 1.1 The unitary duals of SL 2 (R) and SL 4 Introduction In this thesis we present two main results. The first is a Prime Geodesic Theorem for compact symmetric spaces formed as a quotient of the Lie group SL 4 (R). The second is an application of the Prime Geodesic Theorem to prove an asymptotic formula for class n...
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