Related papers: Gamma factors root numbers and distinction

Studying the analytic properties of the partial Langlands $L$-function via Rankin-Selberg method has been proved to be successful in various cases. Yet in few cases is the local theory studied at the archimedean places, which causes a…

In this article, we investigate the variance of local $\varepsilon$-factor for a modular form with arbitrary nebentypus with respect to twisting by a quadratic character. We detect the type of the supercuspidal representation from that. For…

Let $F$ be a non-archimedean local field of characteristic not equal to $2$ and let $E/F$ be a quadratic algebra. We prove the stability of local factors attached to (complex) irreducible admissible representations of $GL(2,E)$ via the…

Let $E$ be a quadratic semisimple extension of a local field $F$ of characteristic zero. We determine explicit relation between gamma factors for Asai representations of $R_{E/F}{\rm GL}_{2/E}$ defined by the Weil-Deligne representations…

In this paper, we prove the fundamental properties of gamma factors defined by Rankin-Selberg integrals of Shimura type for pairs of generic representations $(\pi, \tau)$ of $\mathrm{U}_{2\ell}(F)$ and $\mathrm{GL}_n(E)$ for a local field…

Let $F$ be a totally real field. We study the root numbers $\epsilon(1/2, \pi)$ of self-dual cuspidal automorphic representations $\pi$ of $\mathrm{GL}_{2N}/F$ with conductor $\mathfrak n$ and regular integral infinitesimal character…

Let $F$ be a $p$-adic field and $\pi$ be an irreducible smooth representation of $\textrm{Sp}_{2n}(F)$. In this paper, we show that if $\pi$ and $\pi^\kappa$ are both generic for a common generic character of the maximal unipotent of a…

We give a new construction of tensor product gamma factors for a pair of irreducible representations of $\operatorname{GL}_c\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_k\left(\mathbb{F}_q\right)$. This construction is a finite field…

Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…

Let $\text{E}/\text{F}$ be a quadratic extension of non-Archimedean local fields with odd residual characteristic. In this paper, we give equivalent conditions for a simple supercuspidal representation $\pi$ of $\text{GL}(n, \text{E})$ to…

The Local Converse Problem is to determine how the family of the local gamma factors $\gamma(s,\pi\times\tau,\psi)$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi$ of $\mathrm{GL}_n(F)$, with…

We give an explicit formula for the twisted gamma factor for a pair of irreducible supercuspidal representations of level zero. We also obtain an explicit formula for the unramified base change of level zero supercuspidal representations.

In this paper, we give a precise definition of an analytic $\gamma$-factor of an irreducible representation of a classical group over a local function field of odd characteristic so that it satisfies some notable properties which are enough…

We continue with our study of the non-critical exceptional zeros of Katz' $p$-adic $L$-functions attached to a CM field $K$, following two threads. In the first thread, we redefine our (group-ring-valued) $\mathcal{L}$-invariant associated…

Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual…

This article discusses deviations from the Cohen-Lenstra heuristics when roots of unity are present. In particular, we propose an explanation for the discrepancy between the observed number of cyclic cubic fields whose 2-class group is…

We study the distinction of the Steinberg representation of a split reductive group $G$ with respect to a split symmetric subgroup $H \subset G$. We relate this distinction problem to a problem about the existence of a non-zero harmonic…

We use the Langlands--Shahidi method in order to define the Shahidi gamma factor for a pair of irreducible generic representations of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_m\left(\mathbb{F}_q\right)$. We…

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 study an analytically irreducible algebroid germ (X, 0) of complex singularity by considering the filtrations of its analytic algebra, and their associated graded rings, induced by the divisorial valuations associated to the irreducible…