相关论文: A remark on the geometric Jacquet functor

We generalize the harmonic continuation of the Riemann xi-function to the $n$-dimension case, to obtain the solution to the Dirichlet problem on $\mathbb{R}_{+}^{n+1}.$ We also provide a new expansion for the harmonic continuation of the…

In this thesis, we study the Casselman-Jacquet functor. We discuss a new technical approach which makes the Casselman-Jacquet functor right adjoint to the Bernstein functor. We give an explanation, using D-modules, of the Bruhat filtration…

Through the theory of Jack polynomials we give an iterative method for integral formula of Dunkl-Bessel functions of type $A_{N-1}$ and a partial product formula for it.

By using Jet Calculus as a consistent framework to describe multiparton dynamics we explain the peculiar evolution equation of fracture functions by means of the recently introduced extended fracture functions.

In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.

We study the structure of the Goulden-Jackson-Vakil formula that relates Hurwitz numbers to some conjectural "intersection numbers" on a conjectural family of varieties $X_{g,n}$ of dimension $4g-3+n$. We give explicit formulas for the…

We improve existing estimates of moments of the Riemann zeta function. As a consequence, we are able to derive new estimates for the asymptotic behaviour of $\sum_{N \alpha \le x} \mathfrak{t}_k(\alpha)$, where $N$ stands for the norm of a…

In this paper we try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should to have.

We study the integrable system of first order differential equations $\omega_i(v)'=\alpha_i\,\prod_{j\neq i}\omega_j(v)$, $(1\!\leq i, j\leq\! N)$ as an initial value problem, with real coefficients $\alpha_i$ and initial conditions…

We define an extension of the Ramanujan trigonometric function to arbitrary dimensions, and give the Dirichlet series generating function. The extension was first given by Eckford Cohen long ago. This links directly to visible point vector…

In this paper, we present a unified approach using model category theory and an associative law to compare some classic variants of the geometric realization functor.

Given two positive integers n,r, we define the Gaudin function of level r to be quotient of the numerator of the determinant det(1/ ((x_i-y_j)(x_i-ty_j) ... (x_i-t^r y_j)), i,j=1..n, by the two Vandermonde in x and y. We show that it can be…

We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimen- sional index theorem. We describe the construction given in hep-th/0512293 of a function that can be interpreted as a gravitational effective action on a…

We consider the variance of a function of $n$ independent random variables and provide new inequalities which, in particular, extend previous results obtained for symmetric functions in the i.i.d.~setting. For instance, we obtain various…

We study reductions well suited to compare structures and classes of structures with respect to properties based on enumeration reducibility. We introduce the notion of a positive enumerable functor and study the relationship with…

Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…

We provide sufficient conditions on the components of a vector field, which ensure the existence of Dulac functions depending on special functions for such vector field. We also present some applications and examples in order to illustrate…

We describe a symplectization functor from the Poisson category to the symplectic "category" and we study some of its properties.

We extend Noether's symmetry theorem to the fractional Riemann-Liouville integral functionals of the calculus of variations recently introduced by El-Nabulsi.

We derive an Ehrhart function for symbols from the Euler-MacLaurin formula with remainder.