Related papers: On Level One Cuspidal Bianchi Modular Forms

We show how to efficiently compute Hilbert modular forms as orthogonal modular forms, generalizing and expanding upon the method of Birch.

Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they…

We study the problem of classification of simple transitive 2-representations for the (non-finitary) 2-category of bimodules over the dual numbers. We show that simple transitive 2-representations with finitary apex are necessarily of rank…

We prove an explicit degree formula for certain unitary Deligne-Lusztig varieties. Combining with an alternative degree formula in terms of Schubert calculus, we deduce several algebraic combinatorial identities which may be of independent…

We calculate the dimension of the locus of elliptic surfaces over P^1 with a section and a given Picard number, in the corresponding moduli space.

The study of a self-consistent system of nonlinear spinor and Bianchi type I gravitational fields in presence of a viscous fluid and $\Lambda$ term with the spinor field nonlinearity being some arbitrary functions of the invariants $I$ an…

In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.

We construct the moduli space of cubic surfaces which do not admit a Sylvester form as an arithmetic quotient, and determine the graded ring of modular forms of even weights.

In this work, we are investigating the problem of integrability of Bianchi class A cosmological models. This class of systems is reduced to the form of Hamiltonian systems with exponential potential forms. The dynamics of Bianchi class A…

We study the field of moduli of singular abelian and K3 surfaces. We discuss both the field of moduli over the CM field and over $\Q$. We also discuss non-finiteness with respect to the degree of the field of moduli. Finally, we provide an…

The non-diagonal Bianchi models are studied in the loop framework for their classical and quantum formulation. The expressions of the Ashtekar-Barbero-Immirzi variables and their properties are found to provide a loop quantization of these…

Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

To prove that a modular variety is of general type, there are three types of obstructions: reflective, cusp and elliptic obstructions. In this paper, we give a quantitative estimate of the reflective obstructions for the unitary case. This…

We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.

We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.

This survey discusses hyperbolicity properties of moduli stacks and generalisations of the Shafarevich Hyperbolicity Conjecture to higher dimensions. It concentrates on methods and results that relate moduli theory with recent progress in…

In this paper we study the evolution of spatially homogeneous and anisotropic Bianchi type-I Universe models with the cosmological constant, \Lambda, and filled with nonlinear viscous fluid. The dynamical equations for these models are…

We show that the canonical-lift construction for ordinary elliptic curves over perfect fields of characteristic $p>0$ extends uniquely to arbitrary families of ordinary elliptic curves, even over $p$-adic formal schemes. In particular, the…

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…