Related papers: Hypergeometric Functions and Carlitz Differential …
We establish a link between the basic properties of the discriminant of periodic second-order differential equations and an elementary analysis of Herglotz functions. Some generalizations are presented using the language of self-adjoint…
We briefly review the description of the internal sector of supergravity theories in the language of generalised geometry and how this gives rise to a description of supersymmetric backgrounds as integrable geometric structures. We then…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.
We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…
A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…
We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…
Let $R$ be a local ring of characteristic $p>0$ which is $F$-finite and has perfect residue field. We compute the generalized Hilbert-Kunz invariant for certain modules over several classes of rings: hypersurfaces of finite representation…
We introduce and discuss a variant of Schanuel conjecture in the framework of the Carlitz exponential function over Tate algebras and allied functions. Another purpose of the present paper is to widen the horizons of possible investigations…
An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous $\mathbb F_q$-linear functions are…
A double covering of the proper orthochronous Lorentz group is understood as a complexification of the special unimodular group of second order (a double covering of the 3-dimensional rotation group). In virtue of such an interpretation the…
We describe a new approach to the notion of general hypergeometric functions
This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions may be expanded in sums of pair products of $\,_{2}F_{3}$ functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible…
The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometric functions from the symmetries and other properties of…
We compute the Artin $L$-function of a diagonal hypersurface D_{\lambda} over a finite field associated to a character of a finite group acting on D_{\lambda} , and under some condition, express it in terms of hypergeometric functions and…
We prove a variety of explicit formulas relating special values of generalized hypergeometric functions to lattice sums with four indices of summation. These results are related to Boyd's conjectured identities between Mahler measures and…
In this paper we study properties of hyperholomorphic functions on commutative finite algebras. It is investigated the Cauchy-Riemann type conditions for hyperholomorphic functions. We prove that a hyperholomorphic function on a commutative…
Classical hypergeometric functions are well-known to play an important role in arithmetic algebraic geometry. These functions offer solutions to ordinary differential equations, and special cases of such solutions are periods of…
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…
This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…