Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Fischer, Jürgen
Titre(s) : An Approach to the Selberg Trace Formula via the Selberg Zeta-Function [Texte électronique] / by Jürgen Fischer
Publication : Berlin, Heidelberg : Springer Berlin Heidelberg, 1987
Description matérielle : 1 online resource (iii, 184 pages)
Collection : Lecture Notes in Mathematics ; 1253
Note(s) : 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
Sujet(s) : Selberg, Formule de trace de
Fonctions zêta
Indice(s) Dewey :
512.7 (23e éd.) = Théorie des nombres
Identifiants, prix et caractéristiques : ISBN 9783540393313
Identifiant de la notice : ark:/12148/cb44689369p
Notice n° :
FRBNF44689369
(notice reprise d'un réservoir extérieur)
Table des matières : Introduction ; Basic facts ; The trace of the iterated resolvent kernel ; The entire
function associated with the Selberg zeta-function ; The general Selberg trace formula
; Index ; Index of notations ; References.
