Selberg Zeta and Theta Functions : A Differential Operator Approach Book

	Introduction	9
1	Elliptic Operators, Duality, and Trace Formulas	17
1.1	Bundles and operators	17
1.2	Wave kernels and duality	30
1.3	Harmonic analysis on compact symmetric spaces	38
1.4	The trace formula	49
2	Theta Functions	63
2.1	Theta functions for compact locally symmetric rank-one spaces	63
2.2	Theta functions for surfaces with cusps	70
3	The Selberg Zeta Function	89
3.1	Zeta functions and the geodesic flow	89
3.2	Traces of resolvents	94
3.3	Properties of the Selberg zeta function	105
4	The Ruelle Zeta Function	121
4.1	The functional equations	121
4.2	The behaviour at the central point	128
5	Examples	141
5.1	The function case	141
5.2	Spinors on real hyperbolic manifolds	142
5.3	Differential forms on real and complex hyperbolic manifolds	143
5.4	One-forms on quaternionic hyperbolic manifolds	149
6	Alternative Descriptions of the Singularities	153
6.1	Dynamical Lefschetz formulas	153
6.2	Group cohomology of the principal series	156
	References	159
	Index	166