Results 11 to 20 of about 307 (28)

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

International 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

, 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

Forum 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, Pierre-Henri Chaudouard   +1 more
doaj   +1 more source

Quantum Limits of Eisenstein Series and Scattering states

, 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, Gradshteyn, Holowinsky, Iwaniec, Iwaniec, Jakobson, Koyama, Lindenstrauss, Luo, Meurman, Michel, Morten S. Risager, Nicole Raulf, Petridis, Selberg, Shnirelman, Soundararajan, Titchmarsh, Truelsen, Yiannis N. Petridis, Zelditch, Zelditch   +21 more
core   +1 more source

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

Forum 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

, 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., Risager, Morten Skarsholm   +1 more
core   +2 more sources

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

Forum 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, Paul D. Nelson, Raphael S. Steiner   +2 more
doaj   +1 more source

Eigenfunctions of the Laplacian and associated Ruelle operator

, 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, Bedford T, Bekka M, Bogomolny E B Carioli M, Helgason S, Helgason S, Iwaniec H, Ph Thieullen   +7 more
core   +1 more source

The spectral decomposition of shifted convolution sums

, 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]

, 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