Related papers: Generators for Vector Spaces Spanned by Double Zet…

We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption…

Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we…

Let $D$ and $E$ be subspaces of the tensor product of the finite-dimensional Hilbert spaces $\mathbb{C}^m \otimes \mathbb{C}^n$. We show that the number of product vectors in $D$ with their partial conjugates in $E$ is uniformly bounded…

We continue the study of the Drinfeld double of the Jordan plane, denoted by $\mathcal D$ and introduced in arXiv:2002.02514. The simple finite-dimensional modules were computed in arXiv:2108.13849; it turns out that they factorize through…

In this paper we define a continuous version of multiple zeta functions with double variables. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations…

Let $k$ be a function field of one variable over a finite field with the characteristic not equal to two. In this paper, we consider the prehomogeneous representation of the space of binary quadratic forms over $k$. We have two main…

We provide polynomial upper bounds for the minimal sizes of distal cell decompositions in several kinds of distal structures, particularly weakly $o$-minimal and $P$-minimal structures. The bound in general weakly $o$-minimal structures…

For a grading-restricted vertex superalgebra $V$ and an automorphism $g$ of $V$, we give a linearly independent set of generators of the universal lower-bounded generalized $g$-twisted $V$-module $\widehat{M}^{[g]}_{B}$ constructed by the…

We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension…

For odd $k$, we give a formula for the relations between double zeta values $\zeta(r,k-r)$ with $r$ even. This formula provides a connection with the space of cusp forms on $\mathrm{SL}_2(\mathbb{Z})$. This is the odd weight analogue of a…

We readdress the question of whether any universal upper bound exists on the square mass m^2 of the lightest scalar around a supersymmetry breaking vacuum in generic N=2 gauged supergravity theories for a given gravitino mass m_3/2 and…

We investigate Dirichlet-type series generated by representation functions that count the number of ways an integer can be expressed as a sum of 'k' signed higher even powers. By combining generalized theta generating functions with a…

The graded Specht module $S^\lambda$ for a cyclotomic Hecke algebra comes with a distinguished generating vector $z^\lambda\in S^\lambda$, which can be thought of as a "highest weight vector of weight $\lambda$". This paper describes the…

Let $\mathbb{Z}$ be the integer numbers, $\mathbb{k}$ an algebraically closed field, $\Lambda$ a finite dimensional $\mathbb{k}$-algebra, mod$\Lambda$ the category of finitely generated right modules, proj$\Lambda$ the full subcategory of…

For the standard Drinfeld-Jimbo quantum group ${\rm U}_q(\mathfrak{g})$ associated with a simple Lie algebra $\mathfrak{g}$, we construct explicit generators of the centre $Z({\rm U}_q(\mathfrak{g}))$, and determine the relations satisfied…

The Iwahori-Hecke algebra of type A acts on tensor product space of the natural representation of the quantum superalgebra U_q(gl(m,n)). We show this action of the Hecke algebra and the action of U_q(gl(m,n)) on the same space determine…

We provide a general framework for the realization of powers or functions of suitable operators on Dirichlet spaces. The first contribution is to unify the available results dealing with specific geometries; a second one is to provide new…

Let $k$ be a number field, suppose that $B$ is a central simple division algebra over $k$, and choose any maximal order $\mathcal{D}$ of $B$. The object of this paper is to show that the group $\mathcal{D}_S^*$ of $S$-units of $B$ is…

We study a scalar singlet dark matter (DM) having mass in sub-TeV regime by extending the minimal scalar singlet DM setup by additional vector like fermions. While the minimal scalar singlet DM satisfies the relic and direct detection…

A formula for the dimension of the space of cuspidal modular forms on $\Gamma_0(N)$ of weight $k$ ($k\ge2$ even) has been known for several decades. More recent but still well-known is the Atkin-Lehner decomposition of this space of cusp…