Results 1 to 10 of about 313 (25)

An orthogonality relation for $\mathrm {GL}(4, \mathbb R) $ (with an appendix by Bingrong Huang)

Forum of Mathematics, Sigma, 2021
Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an orthogonality relation on $\mathrm {GL}(1)$) was used by Dirichlet to prove ...
Dorian Goldfeld, Eric Stade, Michael Woodbury   +2 more
doaj   +1 more source

Error term of the mean value theorem for binary Egyptian fractions

Open Mathematics, 2020
In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained.
Xiao Xuanxuan, Zhai Wenguang
doaj   +1 more source

CM-points and Lattice counting on arithmetic compact Riemann surfaces [PDF]

, 2020
Let $X(D,1) =\Gamma(D,1) \backslash \mathbb{H}$ denote the Shimura curve of level $N=1$ arising from an indefinite quaternion algebra of fixed discriminant $D$. We study the discrete average of the error term in the hyperbolic circle problem over Heegner
Alsina, Montserrat, Chatzakos, Dimitrios
core   +3 more sources

Artin formalism for Selberg zeta functions of co-finite Kleinian groups [PDF]

, 2008
Let $\Gamma\backslash\mathbb H^3$ be a finite-volume quotient of the upper-half space, where $\Gamma\subset {\rm SL}(2,\mathbb C)$ is a discrete subgroup.
Brenner, Eliot, Spinu, Florin
core   +2 more sources

Analytic Continuation of Resolvent Kernels on noncompact Symmetric Spaces [PDF]

, 2003
Let X=G/K be a symmetric space of noncompact type and let L be the Laplacian associated with a G-invariant metric on X. We show that the resolvent kernel of L admits a holomorphic extension to a Riemann surface depending on the rank of the symmetric ...
80, Alexander Strohmaier, Araki, Barreto, Gangolli, Gindikin, Guillopé, Helgason, Mazzeo, Miatello, Müller   +10 more
core   +2 more sources

Strongly tempered hyperspherical Hamiltonian spaces

Forum of Mathematics, Sigma
In 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

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 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

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

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