Results 11 to 20 of about 187 (33)

Automorphic forms and rational homology 3–spheres [PDF]

, 2006
We investigate a question of Cooper adjacent to the Virtual Haken Conjecture. Assuming certain conjectures in number theory, we show that there exist hyperbolic rational homology 3–spheres with arbitrarily large injectivity radius.
Calegari, Frank, Dunfield, Nathan M.
core   +6 more sources

Eisenstein Cohomology and ratios of critical values of Rankin-Selberg L-functions

, 2011
This is an announcement of results on rank-one Eisenstein cohomology of GL(N), with N > 1 an odd integer, and algebraicity theorems for ratios of successive critical values of certain Rankin-Selberg L-functions for GL(n) x GL(n') when n is even and n' is
Harder, Guenter, Raghuram, A.
core   +1 more source

Shintani Cocycles on $\GL_{n}$

, 2007
The aim of this paper is to define an n-1-cocycle $\sigma$ on $\GL_{n}(\Q)$ with values in a certain space $\hD$ of distributions on $\A_f^{n}\setminus\{0\}$. Here $\A_f$ denotes the ring of finite ad\`{e}les of $\Q$, and the distributions take values in
Hill, Richard
core   +1 more source

The mod 2 cohomology rings of congruence subgroups in the Bianchi groups [PDF]

, 2019
We provide new tools for the calculation of the torsion in the cohomology of congruence subgroups in the Bianchi groups : An algorithm for finding particularly useful fundamental domains, and an analysis of the equivariant spectral sequence combined with
Berkove, Ethan, Bui, Anh Tuan, Lakeland, Grant, Rahm, Alexander, Schönnenbeck, Sebastian   +4 more
core   +2 more sources

Multiple period integrals and cohomology

, 2015
This work gives a version of the Eichler-Shimura isomorphism with a non-abelian $H^1$ in group cohomology. Manin has given a map from vectors of cusp forms to a noncommutative cohomology set by means of iterated integrals.
Bruggeman, Roelof, Choie, YoungJu
core   +1 more source

Rigid meromorphic cocycles for orthogonal groups

Forum of Mathematics, Sigma
Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real signature and constructed in some instances via a p-adic analogue of Borcherds’ singular theta lift.
Lennart Gehrmann, Henri Darmon, Michael Lipnowski   +2 more
doaj   +1 more source

L-invariants for cohomological representations of PGL(2) over arbitrary number fields

Forum of Mathematics, Sigma
Let $\pi $ be a cuspidal, cohomological automorphic representation of an inner form G of $\operatorname {{PGL}}_2$ over a number field F of arbitrary signature. Further, let $\mathfrak {p}$ be a prime of F such that G is split at
Lennart Gehrmann, Maria Rosaria Pati
doaj   +1 more source

On the Eisenstein cohomology of odd orthogonal groups

, 2011
The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes for maximal ...
Borel, Borel, Cogdell, Deligne, Franke, Franke, Gerald Gotsbacher, Ginzburg, Grbac, Grobner, Harald Grobner, Jiang, Kazdhan, Kim, Kostant, Schwermer, Soudry, Speh, Tadic   +18 more
core   +1 more source

Boundary and Eisenstein Cohomology of $\mathrm{SL}_3(\mathbb{Z})$

, 2020
In this article, several cohomology spaces associated to the arithmetic groups $\mathrm{SL}_3(\mathbb{Z})$ and $\mathrm{GL}_3(\mathbb{Z})$ with coefficients in any highest weight representation $\mathcal{M}_\lambda$ have been computed, where $\lambda ...
Bajpai, Jitendra, Giusti, Matias Moya, Harder, Günter, Horozov, Ivan   +3 more
core   +1 more source

Eisenstein Cohomology for $\mathrm {GL}_N$ and the special values of Rankin–Selberg L-functions over a totally imaginary number field

Forum of Mathematics, Sigma
This article presents new rationality results for the ratios of critical values of Rankin–Selberg L-functions of $\mathrm {GL}(n) \times \mathrm {GL}(n')$ over a totally imaginary field $F.$ The proof is based on a cohomological ...
A. Raghuram
doaj   +1 more source