Related papers: Gamma factors root numbers and distinction

In this paper, we establish the local converse theorem and the stability of local gamma factors for $\Mp_{2n}$ via the precise local theta correspondence between $\Mp_{2n}$ and $\SO_{2n+1}$ over local fields of characteristic not equal to…

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 study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing…

This paper contains an algebraic constructive and self-contained account of the invariance rule of the digital root under division for an arbitrary natural basis representation. Both the cases of repeating and non-repeating fractionals are…

We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…

The Rankin-Selberg method for studying Langlands' automorphic $L$-functions is to find integral representations, involving certain Fourier coefficients of cusp forms and Eisenstein series, for these functions. In this thesis we develop the…

A method to construct in explicit form the generators of the simple roots of an arbitrary finite-dimensional representation of a quantum or standard semisimple algebra is found. The method is based on general results from the global theory…

Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…

We explicitly construct a finite set of separating invariants for the basic $\Ga$-actions. These are the finite dimensional indecomposable rational linear representations of the additive group $\Ga$ of a field of characteristic zero, and…

We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. Using random walks and exit times, we associate to certain subgraphs (domains) a pair of sequences, each of which…

In the present paper we study properties of roots of characteristic polynomials for the linear recurrent formulae (LRF) that govern time series. We also investigate how the values of these roots affect Singular Spectrum Analysis…

Take a bounded symmetric domain $D$ and an arithmetic subgroup $\Gamma$ of ${\rm Aut}(D)$. Take the quotient $D/\Gamma$, compactify and resolve the singularities. We study the fundamental group of the compact complex manifolds that result…

In this article, we study Prasad's conjecture for regular supercuspidal representations based on the machinery developed by Hakim and Murnaghan to study distinguished representations, and the fundamental work of Kaletha on parameterization…

We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric function field Gamma-function are explained…

The degree of the generators of invariant polynomial rings of is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite…

Let $(a_n), (b_n)$ be linear recursive sequences of integers with characteristic polynomials $A(X),B(X)\in \mathbb{Z}[X]$ respectively. Assume that $A(X)$ has a dominating and simple real root $\alpha$, while $B(X)$ has a pair of conjugate…

Let $E$ be a separable quadratic extension of a locally compact field $F$ of positive characteristic. Asai \gamma-factors are defined for smooth irreducible representations \pi of ${\rm GL}_n(E)$. If \sigma is the Weil-Deligne…

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…

In this paper we prove some generalizations of the classical Hasse-Davenport product relation for certain arithmetic factors defined on p-adic fields, among them one finds the epsilon-factors appearing in Tate's thesis. We then show that…

In this work, we explicitly compute a certain family of twisted gamma factors of a simple supercuspidal representation $\pi$ of a $p$-adic odd orthogonal group. These computations, together with analogous computations for general linear…