Related papers: Two functions on Sp(g,R)

The divisor function $\sigma(n)$ denotes the sum of the divisors of the positive integer $n$. For a prime $p$ and $m \in \mathbb{N}$, the $p$-adic valuation of $m$ is the highest power of $p$ which divides $m$. Formulas for…

The matrix-valued spherical functions for the pair (K x K, K), K=SU(2), are studied. By restriction to the subgroup A the matrix-valued spherical functions are diagonal. For suitable set of representations we take these diagonals into a…

In this work we start by determining all irreducible spherical functions $\Phi$ of any $K $-type associated to the pair $(G,K)=(\SO(4),\SO(3))$. The functions $P=P(u)$ corresponding to the irreducible spherical functions of a fixed $K$-type…

A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.

We establish lower bounds on the dimensions in which arithmetic groups with torsion can act on acyclic manifolds and homology spheres. The bounds rely on the existence of elementary p-groups in the groups concerned. In some cases, including…

Inspired by a construction of Bump, Friedberg, and Ginzburg of a two-variable integral representation on $\mathrm{GSp}_4$ for the product of the standard and spin $L$-functions, we give two similar multivariate integral representations. The…

For a finite group $G$, let $\psi(G)$ denote the sum of element orders of $G$. This function was introduced by Amiri, Amiri, and Isaacs in 2009 and they proved that for any finite group $G$ of order $n$, $\psi(G)$ is maximum if and only if…

A set of functions is defined which is indexed by a positive integer $n$ and partitions of integers. The case $n=1$ reproduces the standard Schur polynomials. These functions are seen to arise naturally as a determinant of an action on the…

In this article, the authors establish a general (two-weight) boundedness criterion for a pair of functions, $(F,f)$, on $\mathbb{R}^n$ in the scale of weighted Lebesgue spaces, weighted Lorentz spaces, (Lorentz--)Morrey spaces, and…

We compute the Bernstein-Sato polynomial of $f$, a function which given a pair $(M,v)$ in $X = M_n(\mathbf{C}) \times \mathbf{C}^n$ tests whether $v$ is a cyclic vector for $M$. The proof includes a description of shift operators…

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…

The functional equation f(p(z))=g(q(z)) is studied, where p,q are polynomials and f,g are trancendental meromorphic functions in C. We find all the pairs p,q for which there exist nonconstant f,g satisfying our equation and there exist no…

Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group.

For an integer $M\geq 2$ and a finite group $G$, an element $\alpha\in G$ is called an $M$-th power if it satisfies $A^M=\alpha$ for some $A\in G$. In this article, we will deal with the case when $G$ is finite symplectic or orthogonal…

We extend some definitions and give new results about the theory of slice analysis in several quaternionic variables. The sets of slice functions which are respectively slice, slice regular and circular w.r.t. given variables are…

Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational…

Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson,…

We prove a prime number theorem first for the classical Rankin-Selberg L-function $L(s,\pi\times\pi')$ over any Galois extension with $\pi$ and $\pi'$ unitary automorphic cuspidal representations of $GL_n$ and $GL_m$ respectively with at…

We give a full description of all sets of functions on the group $(\mathbb{ Z}_p, +)$ of prime order which are closed under the composition with the clone generated by $+$ from both sides. Thereby, we also get a description of all iterative…

We present effective algorithms for uniform approximation of multivariate functions satisfying some prescribed inner structure. We extend in several directions the analysis of recovery of ridge functions $f(x)=g(\langle a,x\rangle)$ as…