In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

Kummer type formulas are identities of hypergeometric series. A symmetry by the permutations of n-letters yields these formulas. We will present an algorithmic method to derive known and new Kummer type formulas. The algorithm utilizes several algorithms in algebra and geometry for generating Kummer type formulas.

This paper describes, in detail, a process for constructing Kummer K3 surfaces, and other “generalized” Kummer K3 surfaces. In particular, we look at how some well-known geometrical objects such as the platonic solids and regular polygons can inspire the creation of singular surfaces, and we investigate the resolution of those surfaces. Furthermore, we will extend this methodology to examine th...

In the first part of this paper we give a survey of classical results on Kummer surfaces with Picard number 17 from the point of view of lattice theory. We prove ampleness properties for certain divisors on Kummer surfaces and we use them to describe projective models of Kummer surfaces of (1, d)polarized Abelian surfaces for d = 1, 2, 3. As a consequence we prove that in these cases the Néron–...

We investigate a generalization of Kummer construction, as introduced in [AW08]. The aim of this work is to classify 3-dimensional Kummer varieties by computing their Poincaré polynomials.

Scalar multiplication on Legendre form elliptic curves can be speeded up in two ways. One can perform the bulk of the computation either on the associated Kummer line or on an appropriate twisted Edwards form elliptic curve. This paper provides details of moving to and from between Legendre form elliptic curves and associated Kummer line and moving to and from between Legendre form elliptic cur...

Special matrix functions appear in the literature related to statistics [1-4] and more recently in connection with matrix analogues of Laguerre, Hermite and Legendre differential equations and the corresponding polynomial families [5-7]. The connection between the Humbert matrix function and modified Bessel matrix function has been established in [8,9]. In recent papers [10,11], we defined and ...

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

A Kummer variety is obtained as the quotient of an abelian variety by the automorphism (−1) acting on it. Kummer varieties can be seen as a higher dimensional generalisation of the xcoordinate representation of a point of an elliptic curve given by its Weierstrass model. Although there is no group law on the set of points of a Kummer variety, the multiplication of a point by a scalar still make...