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Field name	Details
Dewey Class	512.7
Title	An Approach to the Selberg Trace Formula via the Selberg Zeta-Function ([EBook] /) / by Jürgen Fischer.
Author	Fischer, Jürgen
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1987.
Physical Details	IV, 188 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1253
ISBN	9783540393313
Summary Note	The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta-function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to known results on classical automorphic forms without the Riemann-Roch theorem. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function. For example, the canonical factorization theorem involves an analogue of the Euler constant. Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-function. Apart from the basic spectral theory of the Laplacian for cofinite groups the book is self-contained and will be useful as a quick approach to the Selberg zeta-function and the Selberg trace formula.:
Contents note	Basic facts -- The trace of the iterated resolvent kernel -- The entire function ? associated with the selberg zeta-function -- The general selberg trace formula.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0077696
Links to Related Works	Subject References: Mathematics . Number Theory . Authors: Fischer, Jürgen . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512.7 .

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An Approach to the Selberg Trace Formula via the Selberg Zeta-Function

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