Related papers: On the number of points with bounded dynamical can…
For one variable rational function $\phi\in K(z)$ over a field $K$, we can define a discrete dynamical system by regarding $\phi$ as a self morphism of $\mathbb{P}_{K}^{1}$. Hatjispyros and Vivaldi defined a dynamical zeta function for this…
This work has two main purposes. On the one side we investigate in this work a question of H. Esnault on congruence formula in a construction of H. Esnault and C. Xu for the number of rational points on the closed fiber of a singular model…
This paper explores the domain of meromorphic extension for the dynamical zeta function associated to a class of one-dimensional differentiable parabolic maps featuring an indifferent fixed point. We establish the connection between this…
In this paper, we investigate the size of moments of quadratic character sums averaged over the family of fundamental discriminants. We obtain an asymptotic formula for all integer moments in a restricted range of parameters using a…
In this manuscript, we consider the Riemann zeta function $\zeta$, defined through the Abel summation formula. We present a simple analytical method based on a complex differential equation. The aim is to propose a new analytical approach,…
We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and…
For several applications in the arithmetic of abelian varieties it is important to compute canonical heights. Following Faltings and Hriljac, we show how the canonical height on the Jacobian of a smooth projective curve can be computed…
We study multiple change point localization under bandit feedback. An unknown piecewise-constant function on a compact interval can be queried sequentially at adaptively chosen inputs, and each query returns a noisy evaluation of the…
This article concerns the computational complexity of a fundamental problem in number theory: counting points on curves and surfaces over finite fields. There is no subexponential-time algorithm known and it is unclear if it can be…
In the paper we discuss two questions about smooth expanding dynamical systems on the circle. (i) We characterize the sequences of asymptotic length ratios which occur for systems with H\"older continuous derivative. The sequences of…
We consider the arithmetic of Henon maps f(x, y)=(ay, x+f(y)) defined over number fields and function fields, usually with the restriction that a=1. We prove a result on the variation of Kawaguchi's canonical height in families of Henon…
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic…
The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number…
We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0,1}. For a class F of boolean functions and a…
There are two approaches to time series approximate factor models: the static factor model, where the factors are loaded contemporaneously by the common component, and the Generalised Dynamic Factor Model, where the factors are loaded with…
We prove that the dynamical zeta function $Z(s)$ associated to $z^2 + c$ with $c < -3.75$ has essential zero-free strips of size $1/2 +$, that is, for every $\epsilon > 0$, there exist only finitely many zeros in the strip $\mathrm{Re}(s) >…
Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…
We give an algorithm which requires no integer factorization for computing the canonical height of a point in $\mathbb{P}^1(\mathbb{Q})$ relative to a morphism $\phi: \mathbb{P}_{\mathbb{Q}}^1 \rightarrow \mathbb{P}_{\mathbb{Q}}^1$ of…
Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…
The article considers the discrete analogue of the method of quickest descent for an inverse Acoustics problem in case of a smooth source. The authors derived the gradient of functional in differential and discrete cases, described the…