Related papers: Degrees of periods
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
What is the period of the Fibonacci sequence modulo a prime? The purpose of our brief expository paper is to illustrate an accessible, motivated treatment of this classical topic using only ideas from linear and abstract algebra (rather…
An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the…
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem…
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these…
We define the tropical Tevelev degrees, $\mathsf{Tev}_g^{trop}$, as the degree of a natural finite morphism between certain tropical moduli spaces, in analogy to the algebraic case. We develop an explicit combinatorial construction that…
We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…
Classifying isomorphism classes of group gradings on algebras presents a compelling challenge, particularly within the realms of non-simple and infinite-dimensional algebras, which have been relatively unexplored. This study focuses on a…
Recent work has shown that the study of supercharacters on abelian groups provides a natural framework within which to study certain exponential sums of interest in number theory. Our aim here is to initiate the study of Gaussian periods…
We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all its…
It is widely known that the minimal free resolution of a module over a complete intersection ring has nice patterns eventually arising in its Betti sequence. In 1997, Avramov, Gasharov, and Peeva defined the notion of critical degree for…
We develop some algebraic structure notions such as composition series and convexity degree, along with some notions holding a geometric interpretation, like reducibility and hyperdimension, with the main objective being a tropical…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
In 2006 Qian [J. Qian, Degree complete graphs; Discrete Mathematics 306 (2006), 533--537] introduced the concept of degree complete graphs for labeled graphs. He also gave a characterization of these graphs in terms of two forbidden…
Given a countable structure $\mathcal{A}$, the degree spectrum of $\mathcal{A}$ is the set of all Turing degrees which can compute an isomorphic copy of $\mathcal{A}$. One of the major programs in computable structure theory is to determine…
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
We survey the theory of Muchnik (weak) and Medvedev (strong) degrees of subsets of ${}^\omega\omega$ with particular attention to the degrees of $\Pi^0_1$ subsets of ${}^\omega2$. Later sections present proofs, some more complete than…
We calculate the degree of the algebra of covariants $\mathcal{C}_d$ for binary $d$-form. Also, for the degree we obtain its integral representation and asymptotic behavior.
We consider series of the form $$ \frac{p}{q} +\sum_{j=2}^\infty \frac{1}{x_j}, $$ where $x_1=q$ and the integer sequence $(x_n)$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for $n\geq 1$.…
We study the transcendence of periods of abelian differentials, both at the arithmetic and functional level, from the point of view of the natural bi-algebraic structure on strata of abelian differentials. We characterise geometrically the…