Related papers: Regulators of K_1 of Hypergeometric Fibrations
We discuss Beilinson's regulator on K_2 of certain fibrations of algebraic varieties which we call the hypergeomtric fibrations. The main result is to describe regulators via the hypergeometric functions 3F2 or 4F3. We also discuss the…
We study periods and regulators of a certain class of fibrations of varieties whose relative $H^1$ has multiplication by a number field. Both are written in terms of values of hypergeometric functions ${}_3F_2$ and the former reduces to…
We give an explicit description of a syntomic regulator of a certain class of fibrations which we call hypergeometric fibrations. The description involves hypergeometric functions.
We study the $H^2$ of certain surfaces with complex multiplication by a cyclotomic field. The periods are written in terms of values of the gamma function and the conjecture of Gross-Deligne is verified. The regulators of certain…
The aim of this work is to study fiber derivatives associated to Lagrangian and Hamiltonian functions describing the dynamics of a higher-order autonomous dynamical system. More precisely, given a function in $T^*T^{(k-1)}Q$, we find…
For certain class of hypergeometric functions ${}_3F_2$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are…
We compute periods of perturbations of a Fermat variety. This allows us to consider a subspace of the Hodge cycles defined by "simple" arithmetic conditions. We explore some examples and give an upper bound for the dimension of this…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
We construct a class of representations of the quadratic R-matrix algebra, given by the reflection equation with the spectral parameter, in terms of certain ordinary difference operators. These operators turn out to act as parameter…
Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper we study the theory of (formal) deformation of…
The goal of this paper is to study the deformations of compact K\"ahler hyperbolic manifolds. We propose slightly modified versions of K\"ahler hyperbolicity as a tool to provide a first step towards investigating the deformation openness…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
We study the behaviour of infinitesimal deformation functors of local group actions with regard to passing to subgroups and quotient groups. Inspired by the cohomological information, we conjecture the existence of a decomposition of a…
We give a certain method for computations of real regulator on K_1 of elliptic surfaces. We also give an examples of a regulator indecomposable element for an elliptic surface with an arbitrary large p_g.
In a recent experiment Lauber et al. have deformed cyclically a microwave resonator and have measured the adiabatic normal-mode wavefunctions for each shape along the path of deformation. The nontrivial observed cyclic phases around a…
In this paper we continue investigation of the hypergeometric function ${}_4F_3(1)$ as the function of its seven parameters. We deduce several reduction formulas for this function under additional conditions that one of the top parameters…
We study geometry of the phase space for finite-dimensional dynamical systems with degenerate Lagrangians. The Lagrangian and Hamiltonian constraint formalisms are treated as different local-coordinate pictures of the same invariant…
In this note, we continue our research on Fourier restriction for hyperbolic surfaces, by studying local perturbations of the hyperbolic paraboloid $z=xy,$ which are of the form $z=xy+h(y),$ where $h(y)$ is a smooth function of finite type.…
In this paper we study the thermodynamics of a crystalline solid by applying q-deformed algebra of Fibonacci oscillators through the generalized Fibonacci sequence of two real and independent deformation parameters q1 and q2. We find a (q1,…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…