Related papers: Cyclotomy and analytic geometry over F_1
Dunkl theory is a far reaching generalization of Fourier analysis and special function theory related to root systems. During the sixties and seventies, it became gradually clear that radial Fourier analysis on rank one symmetric spaces was…
It is well known that Clifford (geometric) algebra offers a geometric interpretation for square roots of -1 in the form of blades that square to minus 1. This extends to a geometric interpretation of quaternions as the side face bivectors…
Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker…
We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\mathbb{C}P(2)$. Let $\{\mathcal{F}_t\}_{t \in \mathbb{D}_{\epsilon}}$ be topological trivial (in $\mathbb{C}^2$) analytic deformation of a…
We point out analogies between (a) the explicit formulas in analytic number theory and transversal index theory, (b) Lichtenbaum's recent conjectures on special values of Hasse-Weil zeta functions and a formula for special values of Ruelle…
Let $\mathbb{F}_q$ be the finite field with $q$ elements and $char(\mathbb{F}_q)$ odd. In this article we will describe completely the dynamics of the map $f(X)=c(X^{q+1}+aX^2)$, for $a=\{\pm1\}$ and $c\in\mathbb{F}_q^*$, over the finite…
One parameter subgroups of the group of hyperbolons of volume one when exploited accurately allow one to define and investigate higher order hyperbolic-trigonometric generalization of corresponding polynomials. In parallel functions of…
In this paper, we give a geometric interpretation of optimal functionals in the context of intersection of symmetry planes and cyclic polytopes. For 1D CFTs, we demonstrate that at given derivative order, the functional is given by a…
A generic method to construct zero-difference functions (ZDFs) on algebraic rings is proposed in this paper. Then this method is used over some rings $\mathbb{Z}_{p^k}$, where $p$ is a prime number and $k\ge 2$ is a positive integer, and…
This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating…
The aim of this project is to attach a geometric structure to the ring of integers. It is generally assumed that the spectrum $\mathrm{Spec}(\mathbb{Z})$ defined by Grothendieck serves this purpose. However, it is still not clear what…
In the first half of twentieth century the theory of complex analytic functions and of their zerosets was fully developed. The definition of holomorphic function has a local nature. Germs of holomorphic functions form a distinguished…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely identify categories that generalise the ordinary categories of…
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…
This work is the first, and main, of the series of papers in progress dedicated to Nienhuis operators, i.e., fields of endomorphisms with vanishing Nijenhuis tensor. It serves as an introduction to Nijenhuis Geometry that should be…
The statement of the Gauss-Bonnet theorem brings up an unexpected form of reflexivity (major concept of philosophy of mathematics), so that geometry contemplates itself in it. It is therefore the revolutionary and multifaceted concept of…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…