Computation of Selberg Zeta Functions on Hecke Triangle Groups
نویسنده
چکیده
In this paper, a heuristic method to compute the Selberg zeta function for Hecke triangle groups, Gq is described. The algorithm is based on the transfer operator method and an overview of the relevant background is given.We give numerical support for the claim that the method works and can be used to compute the Selberg Zeta function on Gq to any desired precision. We also present some numerical results obtained by implementing the algorithm. CONTENTS
منابع مشابه
The Ihara-Selberg zeta function for PGL3 and Hecke operators
A weak version of the Ihara formula is proved for zeta functions attached to quotients of the Bruhat-Tits building of PGL3. This formula expresses the zeta function in terms of Hecke-Operators. It is the first step towards an arithmetical interpretation of the combinatorially defined zeta function.
متن کاملOn the Poles of Rankin-selberg Convolutions of Modular Forms
The Rankin-Selberg convolution is usually normalized by the multiplication of a zeta factor. One naturally expects that the non-normalized convolution will have poles where the zeta factor has zeros, and that these poles will have the same order as the zeros of the zeta factor. However, this will only happen if the normalized convolution does not vanish at the zeros of the zeta factor. In this ...
متن کاملIntroduction to zeta integrals and L-functions for GLn
All known ways to analytically continue automorphic L-functions involve integral representations using the corresponding automorphic forms. The simplest cases, extending Hecke’s treatment of GL2, need no further analytic devices and very little manipulation beyond Fourier-Whittaker expansions. [1] Poisson summation is a sufficient device for several accessible classes of examples, as in Riemann...
متن کاملHierarchy of the Selberg zeta functions
We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.
متن کاملThe Selberg Trace Formula for Hecke Operators on Cocompact Kleinian Groups
We compute the Selberg trace formula for Hecke operators (also called the trace formula for modular correspondences) in the context of cocompact Kleinian groups with finite-dimentional unitary representations. We give some applications to the distribution of Hecke eigenvalues, and give an analogue of Huber’s theorem.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008