Related papers: A note on connecting multiplicative functions defi…
After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.
We obtain multiplicity results for a class of first-order superquadratic Hamiltonian systems and a class of indefinite superquadratic elliptic systems which lead to the study of strongly indefinite functionals. There is no assumption to the…
We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that…
In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…
Multiplicative relations between the roots of a polynomial in $\mathbb{Q}[x]$ have drawn much attention in the field of arithmetic and algebra, while the problem of computing these relations is interesting to researchers in many other…
We construct quantum "az+b" groups for new values of the deformation parameter. Along the way we introduce new special functions and study their analytic properties as well as analyze the commutation relations determined by the choice of…
We prove finite field analogues of integral representations of Appell- Lauricella hypergeometric functions in many variables. We consider certain hypersurfaces having a group action and compute the numbers of rational points associated with…
In his earlier work, the author introduced a group theory question that arises in the study of iterated Galois groups of post-critically finite quadratic polynomials. In this paper, we prove the first non-trivial results on this question.
The main goal of this note is to provide a new proof of a classical result about projectivities between finite abelian groups. It is based on the concept of fundamental group lattice, studied in our previous papers \cite{8} and \cite{9}. A…
We survey a family of polynomials that are very useful in all kinds of power series manipulations, and appearing more frequently in the literature. Applications to formal power series, generating functions and asymptotic expansions are…
We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…
Looking forward to introducing an analysis in Galois Fields, discrete functions are considered (such as transcendental ones) and MacLaurin series are derived by Lagrange's Interpolation. A new derivative over finite fields is defined which…
This work provides an effective algorithm for distinguishing finite quotients between two non-isomorphic finitely generated Fuchsian groups $\Gamma$ and $\Lambda$. It will suffice to take a finite quotient which is abelian, dihedral, a…
Given an integer $M\geq 2$, we deploy the generating function techniques to compute the number of $M$-th roots of identity in some of the well-known finite groups of Lie type, more precisely for finite general linear groups, symplectic…
We examine how closely a multiplicative function resembles an additive function. Given a multiplicative function $g$ and an additive function $f$, we examine the size of the quantity $E(f,g;x)=\# \{n\leq x:f(n)=g(n)\}$. We establish a lower…
Markov chains are used to give a purely probabilistic way of understanding the conjugacy classes of the finite symplectic and orthogonal groups in odd characteristic. As a corollary of these methods one obtains a probabilistic proof of…
We establish lower bounds on the rank of matrices in which all but the diagonal entries lie in a multiplicative group of small rank. Applying these bounds we show that the distance sets of finite pointsets in $\mathbb{R}^d$ generate high…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite fields and we establish new asymptotical and not asymptotical upper bounds about it.
We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and explicit their connection to the `kneading sequence' of the polynomial. We then give recursive presentations by generators and…
For the coordinate algebras of connected affine algebraic groups, we explore the problem of finding a presentation by generators and relations canonically determined by the group structure.