Results 11 to 20 of about 309 (27)
Forum of Mathematics, PiWe 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
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. +1 more
core +2 more sources
On the local $L^2$ -Bound of the Eisenstein series
Forum of Mathematics, SigmaWe 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 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
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Theta functions, fourth moments of eigenforms and the sup-norm problem II
Forum of Mathematics, PiLet 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
Decomposition of splitting invariants in split real groups
, 2010 To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of their endoscopic ...
Agaoka +14 more
core +1 more source
$L^p$-Spectral theory of locally symmetric spaces with $Q$-rank one
, 2007 We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space of non-compact
A. Borel +22 more
core +2 more sources
Distribution of modular symbols for compact surfaces
, 2003 We prove that the modular symbols appropriately normalized and ordered have an asymptotical normal distribution for all cocompact subgroups of SL_2(R).
Risager, Morten Skarsholm
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On pairs of prime geodesics with fixed homology difference [PDF]
, 2006 We exhibit the analogy between prime geodesics on hyperbolic Riemann surfaces and ordinary primes. We present new asymptotic counting results concerning pairs of prime geodesics whose homology difference is fixed.Comment: 19 pages, Corrected typos ...
Risager, Morten S.
core +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 +21 more
core +1 more source