Related papers: On generalized series fields and exponential-logar…
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…
We study solutions of exponential polynomials over the complex field. Assuming Schanuel's conjecture we prove that certain polynomials have generic solutions in the complex field.
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
We review exceptional field theories as the duality-covariant reformulation of maximal supergravity theories in ten and eleven dimensions, that make the underlying exceptional symmetries explicit. Beyond their structural role in unifying…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
The novel concept of box spline of complex degree is introduced and several of its properties derived and discussed. These box splines of complex degree generalize and extend the classical box splines. Relations to a class of fractional…
This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized K\"ahler geometry from sigma models with additional spinorial superfields.…
We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our…
In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F.…
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
We construct, for any finite commutative ring $R$, a family of representations of the general linear group $\mathrm{GL}_n(R)$ whose intertwining properties mirror those of the principal series for $\mathrm{GL}_n$ over a finite field.
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
We introduce some generalizations of the Euler-Kronecker constant of a number field and study their arithmetic nature.
We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.