Related papers: On the number of points with bounded dynamical can…
The traditional method of teaching canonical transformations involves the introduction of generating functions of various types. This method obscures the underlying structure of the Hamiltonian least-action principle, and can make a…
We define arithmetical and dynamical degrees for dynamical systems with several rational maps on projective varieties, study their properties and relations, and prove the existence of a canonical height function associated with divisorial…
The individual terms of the series representing the Riemann zeta function are examined geometrically from their accumulated plot in the complex plane. Symmetry is identified and determined mathematically for comparison with more traditional…
Selection of descent direction at a point plays an important role in numerical optimization for minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a…
We give a conditional lower bound on the number of non-trivial simple zeros for the Dedekind zeta function $\zeta_{K}(s)$, where $K$ is a quadratic number field. The conditional result is given by assuming a Lindel\"of on average (in the…
We present numerical evidence that the dynamical zeta function and the Fredholm determinant of intermittent maps with a neutral fix point have branch point singularities at z=1 We consider the power series expansion of zeta function and the…
In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…
We prove an asymptotic formula as $x\to +\infty$ for the number of algebraic integers $\alpha$ belonging to a fixed CM number field and satisfying $\alpha\overline{\alpha}\leq x$. This problem is related to the height zeta function…
The Riemann zeta function and the distribution of its nontrivial zeros on the critical line remain central topics in analytic number theory and large-scale computation. This work develops a numerical framework that replaces classical…
This paper studies a version of the counting problem in dynamical systems that is of interest, especially in conformal dynamical systems where the functions of the systems are angle preserving. Recently, M. Pollicott and M. Urba\'{n}ski…
The finite Dirichlet series from the title are defined by the condition that they vanish at as many initial zeroes of the zeta function as possible. It turned out that such series can produce extremely good approximations to the values of…
An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski open subset of an arbitrary smooth biquadratic hypersurface in sufficiently many variables. The proof uses…
For a $\mathbb{Z}^d$-action $\alpha$ by commuting homeomorphisms of a compact metric space, Lind introduced a dynamical zeta function that generalizes the dynamical zeta function of a single transformation. In this article, we investigate…
We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over the rationals. The estimate is uniform in the coefficients of the underlying quadratic form.
A method is described to sum multi-dimensional arithmetic functions subject to hyperbolic summation conditions, provided that asymptotic formulae in rectangular boxes are available. In combination with the circle method, the new method is a…
In this work, we propose some numerical schemes for linear kinetic equations in the diffusion and anomalous diffusion limit. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
We establish an asymptotic formula for the number of $\mathcal{M}$-points of bounded height on split toric varieties, for the height induced by any big and nef divisor class. This formula establishes new cases of the extension of Manin's…
Given a number field $K$ of degree $n_K$ and with absolute discriminant $d_K$, we obtain an explicit bound for the number $N_K(T)$ of non-trivial zeros (counted with multiplicity), with height at most $T$, of the Dedekind zeta function…
Let $q$ be an odd prime power, and $H_{d,q}$ denote the set of square-free monic polynomials $D(x) \in F_q[x]$ of degree $d$. Katz and Sarnak showed that the moments, over $H_{d,q}$, of the zeta functions associated to the curves…