Related papers: A Local Trace Formula for the Generalized Shalika …

By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and then we obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace…

Let $\rk$ be a local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $\GL_{2n}(\rk)$. We prove that for all but countably many characters $\chi$ of $\GL_n(\rk)\times \GL_n(\rk)$, the space of…

We study Shalika models for generic unramified representations of $\mathrm{PGU}_{2,2}$ over non-archimedean local fields of characteristic zero. We show that they are unique up to constant by means of the theta correspondence for…

In this work, we present a systematic approach to investigate the existence, multiplicity, and local gradient regularity of solutions for nonlocal quasilinear equations with local gradient degeneracy. Our method involves an interactive…

We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension…

We construct analogues of Rankin--Selberg integrals for Speh representations of the general linear group over a $p$-adic field. The integrals are in terms of the Shalika model and are expected to be the local counterparts of (suitably…

Let (pi,V) be a generic irreducible representation of a general linear group over a p-adic field. Jacquet, Piatetski-Shapiro, and Shalika gave an open compact subgroup K, so that the subspace V^K consisting of v in V fixed by K is…

A globalized version of a trace formula for the Poisson Sigma Model on the disk is presented by using its formal global picture in the setting of the Batalin-Vilkovisky formalism. This global construction includes the concept of zero modes.…

The Casselman-Shalika method is a way to compute explicit formulas for periods of irreducible unramified representations of p-adic groups that are associated to unique models (i.e. multiplicity-free induced representations). We apply this…

In this paper we provide a framework for quantitative statements on distances and measures when studying algebraic varieties and morphisms of algebraic varieties over local fields. We will concentrate on local fields of the type…

Let F be either R or C. Let $(\pi,V)$ be an irreducible admissible smooth \Fre representation of GL(2n,F). A Shalika functional $\phi:V \to \C$ is a continuous linear functional such that for any $g\in GL_n(F), A \in \Mat_{n \times n}(F)$…

We prove a version of the Stokes formula for differential forms on locally convex spaces. The main tool used for proving this formula is the surface layer theorem proved in another paper by the author. Moreover, for differential forms of a…

We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group is compact. Two interesting examples of the quotient…

In this paper, we extend our previous work on the study of local scales of a function to studying local scales on curves and surfaces. In the case of a function f, the local scales of f at x is computed by measuring the deviation of f from…

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…

In this article we study motives corresponding to the moduli stacks of G-shtukas and their local models. In particular we deal with the question of describing their motivic fundamental invariants. As an application, we provide a criterion…

The main result applies to non-degenerate cases of the generalized Lotka-Volterra model. A criterion is given that relates the stability of two fixed points with the associated Schur complement of there respective community matrices.

In this article, we study local models associated to certain Shimura varieties. In particular, we present a resoultion of their singularities. As a consequence, we are able to determine the alternating semisimple trace of the geometric…

We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of…

We define the local trace function for subspaces of $\ltworn$ which are invariant under integer translation. Our trace function contains the dimension function and the spectral function defined by Bownik and Rzeszotnik and completely…