Related papers: Congruence relations satisfied by quaternionic mod…
In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…
Logarithmic conformal field theories are based on vertex algebras with non-semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have…
We show that, in quaternionic geometry, the Ward transform is a manifestation of the functoriality of the basic correspondence between the $\rho$-quaternionic manifolds and their twistor spaces. We apply this fact, together with the Penrose…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
The problem of normalisation of the modular forms in modular invariant lepton and quark flavour models is discussed. Modular invariant normalisations of the modular forms are proposed.
We show that well-chosen Lagrangians for a class of two-dimensional integrable lattice equations obey a closure relation when embedded in a higher dimensional lattice. On the basis of this property we formulate a Lagrangian description for…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
Several sets of quaternionic functions are described and studied. Residue current of the right inverse of a quaternionic function is introduced in particular cases.
The von Neumann type subsystems of $q$-deformed coherent states are considered. The completeness of such subsystems is proved.
This is the report-version of a mini-series of two articles on the foundations of satisfiability of conjunctive normal forms with non-boolean variables, to appear in Fundamenta Informaticae, 2011. These two parts are here bundled in one…
The partition function is known to exhibit beautiful congruences that are often proved using the theory of modular forms. In this paper, we study the extent to which these congruence results apply to the generalized Frobenius partitions…
We define a motive whose realizations afford modular forms (of arbitrary weight) on an indefinite division quaternion algebra. This generalizes work of Iovita--Spiess to odd weights in the spirit of Jordan--Livn\'e. It also generalizes a…
This work presents a family of fiber bundles where the total spaces are associated with holomorphic functions on several complex variables and the basis spaces extend the notion of quaternionic slice regular functions of several…
Here we follow the basic analysis that is common for real and complex variables and find how it can be applied to a quaternionic variable. Non-commutativity of the quaternion algebra poses obstacles for the usual manipulations; but we show…
Grothendieck-Chow motives of quadric hypersurfaces have provided many insights into the theory of quadratic forms. Subsequently, the landscape of motives of more general projective homogeneous varieties has begun to emerge. In particular,…
We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…
In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.
This paper gives an expository account of our experiments concerning relations between modular forms for congruence subgroups of SL(3,Z) and three dimensional Galois representations. The main new result presented here is a calculation of…
There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work arXiv:1803.01830, such partial sums are related to the radial asymptotics of infinite…
We study quadrangular properties of binary relations on a set $X$~--i.e., properties defined on configurations of four elements--~within an agonistic interpretation, where $xRy$ is interpreted as $x$ ``attacks''~$y$. Such relations induce a…