Related papers: An Identity relating Eisenstein series on general …
The work of Bernstein-Zelevinsky and Zelevinsky gives a good understanding of irreducible subquotients of a reducible principal series representation of $GL_n(F)$, $F$ a $p$-adic field (without specifying their multiplicities which is done…
This paper describes a method to find a connection between combinatorial identities and hypergeometric series with a number of examples. Combinatorial identities can often be written as hypergeometric series with unit argument. In a number…
We discuss certain Eisenstein series on arithmetic quotients of loop groups, G^, which are associated to cusp forms on finite-dimensional groups associated with maximal parabolics of G^.
In this paper we propose a construction of generic character sheaves on reductive groups over finite local rings at even levels, whose characteristic functions are higher Deligne--Lusztig characters when the parameters are generic. We…
We prove that if $k$ and $\ell$ are sufficiently large, then all the zeros of the weight $k+\ell$ cusp form $E_k(z) E_{\ell}(z) - E_{k+\ell}(z)$ in the standard fundamental domain lie on the boundary. We moreover find formulas for the…
We present a novel integral representation for a quotient of global automorphic L-functions, the symmetric square over the exterior square. The pole of this integral characterizes a period of a residual representation of an Eisenstein…
In this work, we define a new type of Eisenstein-like series by using Pell-Lucas numbers and call them the Pell-Lucas-Eisenstein Series. Firstly, we show that the Pell-Lucas-Eisenstein series are convergent on their domain. Afterwards we…
Let $\Gamma$ be a geometrically finite Fuchsian group and suppose that $\chi\colon\Gamma\to\mathrm{GL}(V)$ is a finite-dimensional representation with non-expanding cusp monodromy. We show that the parabolic Eisenstein series for $\Gamma$…
We construct local and global metaplectic double covers of odd general spin groups, using the cover of Matsumoto of spin groups. Following Kazhdan and Patterson, a local exceptional representation is the unique irreducible quotient of a…
We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We…
Zagier introduced toroidal automorphic forms to study the zeros of zeta functions: an automorphic form on GL_2 is toroidal if all its right translates integrate to zero over all nonsplit tori in GL_2, and an Eisenstein series is toroidal if…
The pro-isomorphic zeta function of a finitely generated nilpotent group is a Dirichlet generating series that enumerates all finite-index subgroups whose profinite completion is isomorphic to that of the ambient group. We study the…
Higher-order non-holomorphic Eisenstein series associated to a Fuchsian group $\Gamma$ are defined by twisting the series expansion for classical non-holomorphic Eisenstein series by powers of modular symbols. Their functional identities…
Motivated by spectral gluing patterns in the Betti Langlands program, we show that for any reductive group $G$, a parabolic subgroup $P$, and a topological surface $M$, the (enhanced) spectral Eisenstein series category of $M$ is the…
We proof a Garrett-B\"ocherer decomposition of a vector valued Siegel Eisenstein series $E_{l,0}^2$ of genus 2 transforming with the Weil representation of $\text{Sp}_2(\mathbb{Z})$ on the group ring $\mathbb{C}[(L'/L)^2]$. We show that the…
We sketch a proof of a conjecture of [FFKM] that relates the geometric Eisenstein series sheaf with semi-infinite cohomology of the small quantum group with coefficients in the tilting module for the big quantum group.
We study equivariant primitives of Eisenstein series for principal congruence subgroups and show that they are precisely the corresponding non-holomorphic Eisenstein series. We present closed formulas that naturally generalise existing…
We consider a certain family of Kudla-Rapoport cycles on an integral model of a Shimura variety attached to a unitary group of signature (1,1), and prove that the arithmetic degrees of these cycles can be identified with the Fourier…
In previews works, joint with N. Gurevitch, a family of Rankin-Selberg integrals were shown to represent the twisted standard $\mathcal{L}$-function $\mathcal{L}\left(s,\pi,\chi,\mathfrak{st}\right)$ of a cuspidal representation $ \pi$ of…
In this paper, we propose a formula relating certain residues of Eisenstein series on symplectic groups. These Eisenstein series are attached to parabolic data coming from Speh representations. The proposed formula bears a strong similarity…