Related papers: Differential equations, mirror maps and zeta value…
In this paper, we partially extend recent results of Wan concerning the relationship between the zeta functions of a Calabi-Yau hypersurface and its (singular) mirror variety.
Using symbolic summation tools in the setting of difference rings, we prove a two-parametric identity that relates rational approximations to $\zeta(4)$.
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
We construct variants of the Riemann zeta function with convenient properties and make conjectures about their dynamics; some of the conjectures are based on an analogy with the dynamical system of zeta. More specifically, we study the…
This note describes continued fraction representations for the rational approximations to the zeta function recently found by the author. It is tempting to think that these continued fractions might be analysed using a souped up version of…
This paper is closely related to the recent work [BW17] of the same authors and our purpose is to elaborate more on some of the results and methods from [BW17]. More specifically our goal is two-fold. Firstly, we will indicate how a simple…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
We study lower bounds for the Riemann zeta function $\zeta(s)$ along vertical arithmetic progressions in the right-half of the critical strip. We show that the lower bounds obtained in the discrete case coincide, up to the constants in the…
New (infinitely many) rational approximants to \zeta(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A…
In this paper we extend the Zeta function regularization technique, which gives a meaningful solution to divergent power series, in order to assign finite values to divergent integral of certain transcendental functions $f(x)$. The…
The analytical structure of some generalizations of the circle map is given. Also a generalization of off centre reflection is studied. The stability of Ito-Glass coupled map lattice is studied.
We will prove that the zeta function for Ruelle-expanding maps is rational.
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
It is well-known that the Riemann zeta function does not satisfy any exact polynomial differential equation. Here we present numerical evidence for the existence of approximate polynomial dependencies between the values of the alternating…
Starting from a recent result expressing the Lerch zeta function as a fractional derivative, we consider further fractional derivatives of the Lerch zeta function with respect to different variables. We establish a partial differential…
The goal of this survey is to present intimate interactions between four branches of conformal dynamics: iterations of anti-rational maps, actions of Kleinian reflection groups, dynamics generated by Schwarz reflections in quadrature…
The set-theoretical reflection equation and its solutions, the reflection maps, recently introduced by two of the authors, is presented in general and then applied in the context of quadrirational Yang-Baxter maps. We provide a method for…
We study the derivatives of polynomials with equally spaced zeros and find connections to the values of the Riemann zeta-function at the positive even integers.