Related papers: Algebraic transformations of hypergeometric functi…
This goal of the paper is to show that the automorphisms of the complex of curves in a surface are induced by the self-homeomorphisms of the surface except the surface is the 2-holed torus.
Typical properties of measure space automorphisms with respect to the Halmos and Alpern-Tikhonov metrics are discussed.
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…
We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…
By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.
We prove that the bilinear Hilbert transforms and maximal functions along certain general plane curves are bounded from $L^2(\mathbb{R})\times L^2(\mathbb{R})$ to $L^1(\mathbb{R})$.
This is a common introduction to math.RT/0101170, math.RT/0306333, math.RT/0506043, math.RT/0601028. Compared to these references there are new results including (i) a description of a separable closure of an extension of transcendence…
In this paper we investigate arithmetic properties of automorphic forms on the group G' = GL_m/D, for a central division-algebra D over an arbitrary number field F. The results of this article are generalizations of results in the split…
We consider symmetry operations on the four-dimensional vector space that is spanned by the local versions of the Minkowski functionals (or fundamental measures): volume, surface, integral mean curvature, and Euler characteristic, of an…
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…
This is a first part of a series of papers in which we develop explicit computational methods for automorphic forms for GL(3) and PGL(3) over elliptic function fields. In this first part, we determine explicit formulas for the action of the…
We show that properties of hypergeometric type equations become transparent if they are derived from appropriate 2nd order partial differential equations with constant coefficients. In particular, we deduce the symmetries of the…
In this paper we study algebraic structures of the classes of the $L_2$ analytic Fourier-Feynman transforms on Wiener space. To do this we first develop several rotation properties of the generalized Wiener integral associated with Gaussian…
The paper is devoted to 2-local derivations and 2-local automorphisms on the algebra $B(H)$ of all bounded linear operators on a Hilbert space $H.$ We prove that every 2-local derivation on $B(H)$ is a derivation. A similar result is…
In this paper we discuss some of the recent developments on derived equivalences in algebraic geometry.
We produce first examples of p-local height three TAF homology theories. The corresponding one-dimensional formal groups arise as split summands of the formal groups of certain abelian three-folds, the Shimura variety of which can be…
Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that their values are traces of Frobenius on…
Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the…
Recently, there emerges different versions of beta function and hypergeometric functions containing extra parameters. Gaining enlightenment from these ideas, we will first introduce a new extension of generalized hypergeometric function and…