The Selberg Trace formula and the Ruelle Zeta function for compact hyperbolics

1989 ◽  
Vol 59 (1) ◽  
pp. 101-106 ◽  
Author(s):  
A. Deitmar
Keyword(s):  
Zeta Function ◽  
Trace Formula ◽  
Selberg Trace Formula ◽  
Ruelle Zeta Function

scholarly journals The Selberg trace formula for modular correspondences

1990 ◽  
Vol 117 ◽  
pp. 93-123
Author(s):  
Shigeki Akiyama ◽  
Yoshio Tanigawa
Keyword(s):  
Zeta Function ◽  
Kernel Function ◽  
Trace Formula ◽  
Conjugacy Classes ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Selberg Trace Formula ◽  
Weight One ◽  
Space Of Cusp Forms

In Selberg [11], he introduced the trace formula and applied it to computations of traces of Hecke operators acting on the space of cusp forms of weight greater than or equal to two. But for the case of weight one, the similar method is not effective. It only gives us a certain expression of the dimension of the space of cusp forms by the residue of the Selberg type zeta function. Here the Selberg type zeta function appears in the contribution from the hyperbolic conjugacy classes when we write the trace formula with a certain kernel function ([3J, [4], [7], [8], [9], [12]).

scholarly journals Selberg's trace formula on thek-regular tree and applications

2003 ◽  
Vol 2003 (8) ◽  
pp. 501-526 ◽  
Author(s):  
Audrey Terras ◽  
Dorothy Wallace
Keyword(s):  
Asymptotic Formula ◽  
Zeta Function ◽  
Trace Formula ◽  
Geodesic Flow ◽  
Prime Number Theorem ◽  
Selberg Trace Formula ◽  
Regular Tree ◽  
Graph Theoretic ◽  
Upper Half Plane ◽  
The Laplace Operator

We survey graph theoretic analogues of the Selberg trace and pretrace formulas along with some applications. This paper includes a review of the basic geometry of ak-regular treeΞ(symmetry group, geodesics, horocycles, and the analogue of the Laplace operator). A detailed discussion of the spherical functions is given. The spherical and horocycle transforms are considered (along with three basic examples, which may be viewed as a short table of these transforms). Two versions of the pretrace formula for a finite connectedk-regular graphX≅Γ\Ξare given along with two applications. The first application is to obtain an asymptotic formula for the number of closed paths of lengthrinX(without backtracking but possibly with tails). The second application is to deduce the chaotic properties of the induced geodesic flow onX(which is analogous to a result of Wallace for a compact quotient of the Poincaré upper half plane). Finally, the Selberg trace formula is deduced and applied to the Ihara zeta function ofX, leading to a graph theoretic analogue of the prime number theorem.

scholarly journals A Selberg trace formula for hypercomplex analytic cusp forms

2015 ◽  
Vol 148 ◽  
pp. 398-428 ◽  
Author(s):  
D. Grob ◽  
R.S. Kraußhar
Keyword(s):  
Trace Formula ◽  
Cusp Forms ◽  
Selberg Trace Formula

scholarly journals SEIBERG–WITTEN PREPOTENTIAL FROM WZNW CONFORMAL BLOCK: LANGLANDS DUALITY AND SELBERG TRACE FORMULA

2012 ◽  
Vol 27 (22) ◽  
pp. 1250129
Author(s):  
TA-SHENG TAI
Keyword(s):  
Trace Formula ◽  
Conformal Block ◽  
Selberg Trace Formula ◽  
Conformal Blocks ◽  
Langlands Duality

We show how SU(2) Nf = 4 Seiberg–Witten prepotentials are derived from [Formula: see text] four-point conformal blocks via considering Langlands duality.

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