Results 21 to 30 of about 357 (64)
Maass cusp forms for large eigenvalues [PDF]
, 2003 We investigate the numerical computation of Maass cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r=40000.
Then, H.
core +5 more sources
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
Strongly tempered hyperspherical Hamiltonian spaces
Forum of Mathematics, SigmaIn this paper, we give a complete list of strongly tempered anomaly-free hyperspherical Hamiltonian spaces-those that are dual to symplectic vector spaces under the relative Langlands duality.
Zhengyu Mao, Chen Wan, Lei Zhang
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 +21 more
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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
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$L^p$-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
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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.
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Invariant four-variable automorphic kernel functions [PDF]
, 2015 Let $F$ be a number field, let $\mathbb{A}_F$ be its ring of adeles, and let $g_1,g_2,h_1,h_2 \in \mathrm{GL}_2(\mathbb{A}_F)$. Previously the author provided an absolutely convergent geometric expression for the four variable kernel function $$ \sum_ ...
Getz, Jayce R.
core
Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space
, 2018 For $\Gamma$ a cofinite Kleinian group acting on $\mathbb{H}^3$, we study the Prime Geodesic Theorem on $M=\Gamma \backslash \mathbb{H}^3$, which asks about the asymptotic behaviour of lengths of primitive closed geodesics (prime geodesics) on $M$.
Balkanova, Olga +4 more
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