相关论文: CM periods, CM regulators and hypergeometric funct…
We study the Heckman-Opdam hypergeometric functions associated to a root system of type $BC$ and a multiplicity function which is allowed to assume some non-positive values (a standard multiplicity function). For such functions, we obtain…
The A-hypergeometric system studied by I.M. Gelfand, M.I. Graev, A.V. Zelevinsky and the author, is defined for a set A of characters of an algebraic torus. In this paper we propose a generalization of the theory where the torus is replaced…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
We introduce fibrewise compactifications in both the setting of locally compact Hausdorff spaces and continuous maps, and the parallel setting of $C^*$-algebras and nondegenerate multiplier-valued $*$-homomorphisms. In both situations, we…
Several expansions of the solutions of the double-confluent Heun equation in terms of the Kummer confluent hypergeometric functions are presented. Three different sets of these functions are examined. Discussing the expansions without a…
Analytical Hartree-Fock gradients with respect to the cell parameter have been implemented in the electronic structure code CRYSTAL, for the case of one and two-dimensional periodicity. As in most molecular codes, Gaussian type orbitals are…
Value of generalized hypergeometric function at a special point is calculated. More precisely, value of certain multiple integral over vanishing cycle (all arguments collapse to unity) is calculated. The answer is expressed in terms of…
I study the gauge-invariant fluctuations of the metric during inflation. In the infrared sector the metric fluctuations can be represented by a coarse-grained field. We can write a Schroedinger equation for the coarse-grained metric…
Darboux-deformations of short range one-dimensional potentials are constructed by means of Gamow-Siegert functions (resonance states). Results include both Hermitian and non-Hermitian short range potentials which are exactly solvable. As…
These are (somewhat informal) lectures notes for the CIME summer school "Geometric Representation Theory and Gauge Theory" in June 2018. In these notes we review the results and constructions of a series of our joint papers with H.Nakajima…
In this part of the series, we shall investigate Deligne-Mumford semistable reductions from the point of view of numerical invariants. As an application, we obtain two numerical criterions for a base change to be stabilizing, and for a…
We study the geometry of $m$-regular domains within the Caffarelli-Nirenberg-Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every $m$-hyperconvex domain…
In the recent years a lot of effort has been made to extend the theory of hyperholomorphic functions from the setting of associative Clifford algebras to non-associative Cayley-Dickson algebras, starting with the octonions. An important…
We prove inequalities that compare the relative regulator of an extension of number fields with a product of heights of multiplicatively independent relative units.
In this paper, we obtain recursion formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function. We also give finite and infinite summation formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function.
We find two-sided inequalities for the generalized hypergeometric function of the form ${_{q+1}}F_{q}(-x)$ with positive parameters restricted by certain additional conditions. Both lower and upper bounds agree with the value of…
We analyze degenerate, second-order, elliptic operators $H$ in divergence form on $L_2({\bf R}^{n}\times{\bf R}^{m})$. We assume the coefficients are real symmetric and $a_1H_\delta\geq H\geq a_2H_\delta$ for some $a_1,a_2>0$ where \[…
We derive all eighteen Gauss hypergeometric representations for the Ferrers function of the second kind, each with a different argument. They are obtained from the eighteen hypergeometric representations of the associated Legendre function…
The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are…
The standard literature on special functions contains a lot of hypergeometric identities involving products and quotients of gamma functions, but still the occurrence of such identities is a sporadic phenomenon. This is because the…