Related papers: Integer Matrix Exact Covering Systems and Product …
We show that any infinite collection $(\Gamma_n)_{n\in \mathbb N}$ of icc, hyperbolic, property (T) groups satisfies the following von Neumann algebraic \emph{infinite product rigidity} phenomenon. If $\Lambda$ is an arbitrary group such…
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…
We consider the reproducing kernel function of the theta Bargmann-Fock Hilbert space associated to given full-rank lattice and pseudo-character, and we deal with some of its analytical and arithmetical properties. Specially, the…
On the set of mappings of the given set, we define the product of mappings. If A is associative algebra, then we consider the set of matrices, whose elements are linear mappings of algebra A. In algebra of matrices of linear mappings we…
By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…
We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two elementary blocks it is possible to represent these relations in a…
For an arbitrary positive integer $p$, Landen's formula is extended to express theta function with modulus $p\tau$ by $p$ product of theta functions with $\tau$, which is applied to several examples. Next it is shown that double product of…
Kang et al. provided a path realization of the crystal graph of a highest weight module over a quantum affine algebra, as certain semi-infinite tensor products of a single perfect crystal. In this paper, this result is generalized to give a…
We determine the special values at positive integers of the spectral zeta function associated with the combinatorial Laplacian on the regular tree. These values admit explicit formulas in terms of certain polynomials, which we show to be…
We consider a certain linear combination $S(\mathbf{s},\mathbf{y};I;\Delta)$ of zeta-functions of root systems, where $\Delta$ is a root system of rank $r$ and $I\subset\{1,2,\ldots,r\}$. Showing two different expressions of…
We study q-integral representations of the q-gamma and the q-beta functions. This study leads to a very interesting q-constant. As an application of these integral representations, we obtain a simple conceptual proof of a family of…
Using the notions and tools from realization in the sense of systems theory, we establish an explicit and new realization formula for families of infinite products of rational matrix-functions of a single complex variable. Our realizations…
We show how two iterated products of selection functions can both be used in conjunction with system T to interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated…
This manuscript introduces a general multisection identity expressed equivalently in terms of infinite double products and/or infinite double series, from which several new product or summation identities involving special functions…
In this paper we prove trace formulae for the Reidemeister number of a group endomorphism. This result implies the rationality of the Reidemeister zeta function in the following cases: the group is a direct product of a finite group and a…
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory…
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…
We show that the mathematical structures in a recent work of Bultinck-Mariena-Williamson-Sahinoglu-Haegemana-Verstraete are the same as those of flat symmetric bi-unitary connections and the tube algebra in subfactor theory. More…
We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following…
The theta series of a lattice is a power series that characterizes the number of lattice vectors at certain norms. It is closely related to a critical quantity widely used in physical layer security and cryptography, known as the flatness…