Related papers: A note on gamma factors for pairs

We prove that the local Rankin--Selberg integrals for principal series representations of the general linear groups agree with certain simple integrals over the Rankin--Selberg subgroups, up to certain constants given by the local gamma…

Let $(\pi,V)$ be a $GL_n(\mathbb{R})$-distinguished, irreducible, admissible representation of $GL_n(\mathbb{C})$, let $\pi'$ be an irreducible, admissible, $GL_m(\mathbb{R})$-distinguished representation of $GL_m(\mathbb{C})$, and let…

Let $F$ be a $p$-adic field and choose $k$ an algebraic closure of $\mathbb{F}_{\ell}$, with $\ell$ different from $p$. We define ``nilpotent lifts'' of irreducible generic $k$-representations of $GL_n(F)$, which take coefficients in Artin…

We introduce graded gamma rings from a more general point of view via methods developed by Krasner and Halberstadt for graded rings. We propose three equivalent aspects of studying graded gamma rings, nonhomogeneous, semihomogeneous and…

The aim of this paper is to determine all algebraic relations among various special gamma values over function fields, and prove a Chowla-Selberg-type formula for quasi-periods of CM abelian $t$-modules. Our results are based on the…

Let $\Gamma$ be a finite group. Consider the wreath product $G_n := \Gamma^n \rtimes S_n$ and the subgroup $K_n := \Delta_n \times S_n\subseteq G_n$, where $S_n$ is the symmetric group and $\Delta_n$ is the diagonal subgroup of $\Gamma^n$.…

Let $\pi$ and $\tau$ be a smooth generic representation of ${\rm SO}_5$ and ${\rm GL}_2$ respectively over a non-archimedean local field. Assume that $\pi$ is irreducible and $\tau$ is irreducible or induced of Langlands' type. We show that…

We follow Jacquet-Shalika, Matringe and Cogdell-Matringe to define exterior square gamma factors for irreducible cuspidal representations of $\mathrm{GL}_n(\mathbb{F}_q)$. These exterior square gamma factors are expressed in terms of Bessel…

Let $G=\mathrm{SL}(3,\mathbb{C})$. We construct an element of $G$-equivariant $K$-homology from the Bernstein-Gelfand-Gelfand complex for $G$. This furnishes an explicit splitting of the restriction map from the Kasparov representation ring…

This article addresses the problem of existence of local factors, i.e., the root numbers and L-functions attached to representations of reductive groups over local fields and irreducible finite dimensional representations of their L-groups,…

We give a new proof of the stability of the symmetric cube gamma factor as defined by the Langlands-Shahidi method.

As a generalization of the results [KW3],we study the functional equation of the higher Selberg zeta function for congruence subgroups. To obtain the gamma factor of this function, we introduce a higher Dirichlet $L$-function. Then we…

In this article, we construct a family of integrals which represent the product of Rankin-Selberg $L$-functions of $\mathrm{GL}_{l}\times \mathrm{GL}_m$ and of $\mathrm{GL}_{l}\times \mathrm{GL}_n $ when $m+n<l$. When $n=0$, these integrals…

In analogy with values of the classical Euler Gamma-function at rational numbers and the Riemann zeta-function at positive integers, we consider Thakur's geometric Gamma-function evaluated at rational arguments and Carlitz zeta-values at…

We introduce Riemann operators acting on Quillen's higher $K$--groups $K_{n}(A)$ for the integer ring $A$ of an algebraic number field $K$. Especially we prove that gamma factors of Dedekind zeta function of $K$ are obtained as regularized…

Let $E$ is be vector bundle with meromorphic connection on $\proj^1/k$ for some field $k \subset \cplx$, and let $\mathbf{E}$ be the sheaf of horizontal sections on the analytic points of $X$. The irregular Riemann-Hilbert correspondence…

We establish the existence and uniqueness of twisted exterior and symmetric square $\gamma$-factors in positive characteristic by studying the Siegel Levi case of generalized spinor groups. The corresponding theory in characteristic zero is…

This is the last version of AG/0111277. Here the old abstract: We define $\epsilon$-factors in the de Rham setting and calculate the determinant of the Gau\ss-Manin connection for a family of (affine) curves and a vector bundle equipped…

The applications of the consistently coupled Schwinger-Dyson and Bethe-Salpeter approach to the eta-eta' complex are extended to the two-photon transition form factors of eta and eta' for spacelike transferred momenta. We compare our…

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…