Results 11 to 20 of about 307 (28)

Selberg′s trace formula on the k‐regular tree and applications

open access: yesInternational Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 8, Page 501-526, 2003., 2003
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 a k‐regular tree Ξ (symmetry group, geodesics, horocycles, and the analogue of the Laplace operator). A detailed discussion of the spherical functions is given.
Audrey Terras, Dorothy Wallace
wiley   +1 more source

On uniform lattices in real semisimple groups

open access: yes, 2015
In this article we prove that the co-compactness of the arithmetic lattices in a connected semisimple real Lie group is preserved if the lattices under consideration are representation equivalent.
Bhagwat, Chandrasheel, Pisolkar, Supriya
core   +1 more source

The global Gan-Gross-Prasad conjecture for unitary groups. II. From Eisenstein series to Bessel periods

open access: yesForum of Mathematics, Pi
We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$ .
Raphaël Beuzart-Plessis   +1 more
doaj   +1 more source

Quantum Limits of Eisenstein Series and Scattering states

open access: yes, 2013
We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line.
Colin de Verdiére   +21 more
core   +1 more source

On the local $L^2$ -Bound of the Eisenstein series

open access: yesForum of Mathematics, Sigma
We study the growth of the local $L^2$ -norms of the unitary Eisenstein series for reductive groups over number fields, in terms of their parameters. We derive a poly-logarithmic bound on an average, for a large class of reductive groups.
Subhajit Jana, Amitay Kamber
doaj   +1 more source

The distribution of values of the Poincare pairing for hyperbolic Riemann surfaces

open access: yes, 2004
For a cocompact group of SL_2(R) we fix a non-zero harmonic 1-form \a. We normalize and order the values of the Poincare pairing according to the length of the corresponding closed geodesic l(gamma).
Petridis, Yiannis N.   +1 more
core   +2 more sources

Theta functions, fourth moments of eigenforms and the sup-norm problem II

open access: yesForum of Mathematics, Pi
Let f be an $L^2$ -normalized holomorphic newform of weight k on $\Gamma _0(N) \backslash \mathbb {H}$ with N squarefree or, more generally, on any hyperbolic surface $\Gamma \backslash \mathbb {H}$ attached to an Eichler order of ...
Ilya Khayutin   +2 more
doaj   +1 more source

Eigenfunctions of the Laplacian and associated Ruelle operator

open access: yes, 2008
Let $\Gamma$ be a co-compact Fuchsian group of isometries on the Poincar\'e disk $\DD$ and $\Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $\Delta$, equivariant by $\Gamma$ with real eigenvalue $\lambda=-s(1-s ...
A O Lopes   +7 more
core   +1 more source

The spectral decomposition of shifted convolution sums

open access: yes, 2007
We obtain a spectral decomposition of shifted convolution sums in Hecke eigenvalues of holomorphic or Maass cusp forms.Comment: 15 pages, LaTeX2e; v2: corrected and slightly expanded ...
Blomer, Valentin, Harcos, Gergely
core   +1 more source

Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function [PDF]

open access: yes, 2010
AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37We point out the importance of the integral representations of the logarithmic derivative of the Selberg zeta function valid up to the critical line, i.e.
Gušić, Dženan
core  

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