Related papers: On finiteness of spectral radius order
The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE. We consider the spectra obtained by limiting…
In this paper we study the joint/generalized spectral radius of a finite set of matrices in terms of its rank-one approximation by singular value decomposition. In the first part of the paper, we show that any finite set of matrices with at…
We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…
We provide examples of groups with transcendental spectral radius: We first construct finitely presented examples, using links between decidability of the Word Problem and semi-computability of the spectral radius. This argument extends to…
The spectra of a finite group is the set of its element orders. We obtain an arithmetic description of finite symplectic and orthogonal groups. In particular, a description of spectra of all finite simple simplectic and orthogonal groups is…
It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the…
It is shown that the sum of class numbers of orders in totally complex quartic fields with no real quadratic subfield obeys an asymptotic law similar to the prime numbers, as the bound on the regulators tends to infinity. Here only orders…
By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded…
In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.
The problem of phase retrieval is a difficult one which remains far from solved. Two homometric sets are always connected by way of a convolution product by some spectral unit, though not necessarily in a unique way. Here we elucidate one…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
We give a classification and complete algebraic description of groups allowing only finitely many (left multiplication invariant) circular orders. In particular, they are all solvable groups with a specific semi-direct product…
We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic fields. In contrast, we construct infinite degree totally…
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
The spectral radius and rank of a graph are defined to be the spectral radius and rank of its adjacency matrix, respectively. It is an important problem in spectral extremal graph theory to determine the extremal graph that has the maximum…
We consider "cubes" in products of finite cyclic groups and we study their tiling and spectral properties. (A set in a finite group is called a tile if some of its translates form a partition of the group and is called spectral if it admits…
We define notions of higher order spectra of a complex quasi-projective manifold with an action of a finite group $G$ and with a $G$-equivariant automorphism of finite order, some of their refinements and give Macdonald type equations for…
Spectral computations of infinite-dimensional operators are notoriously difficult, yet ubiquitous in the sciences. Indeed, despite more than half a century of research, it is still unknown which classes of operators allow for computation of…
Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements.…
We answer a question posed by Y. Elias et al. in [8] about possible spectral distortions of algebraic numbers. We provide a closed form for the spectral distortion of certain classes of cyclotomic polynomials. Moreover, we present a bound…