Related papers: Une introduction aux p\'eriodes

We develop a $p$-adic theory of periods for 1-motives, extending the classical theory of complex periods into the non-archimedean setting. For 1-motives with good reduction over $p$-adic local fields, we construct a $p$-adic integration…

This is an introduction to $p$-adic geometry and $p$-adic analysis focusing on the theme of $p$-adic period mappings. We follow as closely as possible the development of the classical theory of complex period mappings, blending differential…

Models of period variations are basic tools for period analyzes of variable stars. We introduce phase function and instant period and formulate basic relations and equations among them. Some simple period models are also presented.

Mathematical formula describing the periodicity of the elements in the periodic system is presented.

We discuss how basic notions of graph theory and associated graph polynomials define questions for algebraic geometry, with an emphasis given to an analysis of the structure of Feynman rules as determined by those graph polynomials as well…

The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…

We introduce a new notion of computable function on $\R^N$ and prove some basic properties. We give two applications, first a short proof of Yoshinaga's theorem that periods are \el (they are actually low). We also show that the low complex…

We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical…

We present period domains of complex Hodge structures and some of their basic properties from representation theory point of view. Specifically we introduce the automorphic cohomology of period domains and the complex structure on symmetric…

A class number formula is proved for extended ring class fields $L_{\mathcal{O},9}$ over imaginary quadratic fields $K_d = \mathbb{Q}(\sqrt{-d})$, in which the prime $p = 3$ splits, by determining the fields generated by the periodic points…

We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

We deal with the algebraicity of an iterated Puiseux series in several variables in terms of the properties of its coefficients. Our aim is to generalize to several variables the results from [HM15]. We show that the algebraicity of such a…

By means of the shift operators we introduce a new periodicity concept on time scales. This new approach will enable researchers to investigate periodicity notion on a large class of time scales whose members may not satisfy the condition:…

Periodicity analysis of sequences generated by a deterministic system is a long-standing challenge in both theoretical research and engineering applications. To overcome the inevitable degradation of the Logistic map on a finite-precision…

For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…

The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.

Any rational number can be written as the sum of distinct unit fractions. In this survey paper we review some of the many interesting questions concerning such 'Egyptian fraction' decompositions, and recent progress concerning them.

The purpose of this note is give some evidence in support of conjectures of Poonen, and Morton and Silverman, on the periods of rational numbers under the iteration of quadratic polynomials. In particular, Poonen conjectured that there are…

Building on work of Doyle and Hyde on polynomial maps in one variable, we produce for each odd integer $d \geq 2$ a H\'enon map of degree $d$ defined over $\mathbb{Q}$ with at least $(d-4)^2$ integral periodic points. This provides a…