Related papers: The Selberg Trace Formula IX: Contribution from th…

We added an additional result (theorem 1.6) that strengthenns our main theorem in the G=GL-case by establishing an equivalence of tensor categories.

We provide a short and simple proof of a beautiful result of Kaczorowski and Perelli classifying the elements of degree one in the Selberg class.

We continue the investigation of tabular algebras with trace (a certain class of associative ${\Bbb Z}[v, v^{-1}]$-algebras equipped with distinguished bases) by determining the extent to which the tabular structure may be recovered from a…

In a previous paper, we obtained a general trace formula for double coset operators acting on modular forms for congruence subgroups, expressed as a sum over conjugacy classes. Here we specialize it to the congruence subgroups $\Gamma_0(N)$…

We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of…

We study a class obtained from the Segre class $s(Z,Y)$ of an embedding of schemes by incorporating the datum of a line bundle on $Z$. This class satisfies basic properties analogous to the ordinary Segre class, but leads to remarkably…

In this note, we classify the conjugacy classes of $\widetilde{\mathrm{SL}}_2(\mathbb{R})$, the universal covering group of $\mathrm{PSL}_2(\mathbb{R})$. For any non-central element $\alpha \in \widetilde{\mathrm{SL}}_2(\mathbb{R})$, we…

We extend Venkatesh's proof of the converse theorem for classical holomorphic modular forms to arbitrary level and character. The method of proof, via the Petersson trace formula, allows us to treat arbitrary degree 2 gamma factors of…

We extend the notion of induced conjugacy classes in reductive groups, introduced by Lusztig and Spaltenstein for unipotent classes, to arbitrary classes. We study properties of equivariant fibrations of prehomogeneous affine spaces,…

This note complements a recent paper of Chatzakos, Harcos and Kaneko \cite{CHK}. We use a Dirichlet style Prime Geodesic Theorem to improve the error term estimate in loc. cit. at the cost of lowering the resolution. The proof relies on the…

Let G be a unitary group of a signed-Hermitian form h given over a non-Archimedian local field k of residue characteristic not two. Let V be the vector space on which h is defined. We consider minimal skew-strata, more precisely pairs (b,a)…

Suppose $G$ is a connected complex semisimple group and $W$ is its Weyl group. The lifting of an element of $W$ to $G$ is semisimple. This induces a well-defined map from the set of elliptic conjugacy classes of $W$ to the set of semisimple…

In this paper, we study Siegel modular forms with extra twists. We provide conditions on the level and genus of the forms that is necessary for the existence of extra twists for Siegel modular forms. We also give explicit examples of Siegel…

We establish a one-to-one correspondence between conjugacy classes of any Hecke group and irreducible systems of poles of rational period functions for automorphic integrals on the same group. We use this correspondence to construct…

In this note we present an $\infty$-categorical framework for descent along adjunctions and a general formula for counting conjugates up to equivalence which unifies several known formulae from different fields.

We define and study a correspondence between the set of distinguished G^0-conjugacy classes in a fixed connected component of a reductive group G (with G^0 almost simple) and the set of (twisted) elliptic conjugacy classes in the Weyl…

Properties of relative traces and symmetrizing forms on chains of cyclotomic and affine Hecke algebras are studied. The study relies on a use of bases of these algebras which generalize a normal form for elements of the complex reflection…

We extend a result of Ahlgren and Ono on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.

Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L^2(G/H) associated to test…

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a…