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Axioms
Special Issues
Advances in Number Theory and Applications
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Advances in Number Theory and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 2376

Special Issue Editor

Prof. Dr. Oliver Stein

E-Mail Website
Guest Editor
Fakultät für Informatik und Mathematik, Ostbayerische Technische Hochschule Regensburg, Galgenbergstrasse 32, 93053 Regensburg, Germany
Interests: number theory; modular forms; automorphic forms; cryptography; mathematical cryptography; computation of elliptic curves and modular surfaces for cryptographic purposes
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to collect high-quality original research articles and reviews in advanced perspectives of mathematics.

It covers all aspects of number theory and related research areas. Therefore, contributions on a wide range of subtopics of number theory will be welcomed. Additionally, articles from other mathematical branches in pure and applied mathematics featuring applications of number theory will be published. This includes algebra, algebraic and arithmetic geometry, analysis, mathematical physics, cryptography, computer science, etc.

Many of the most interesting questions in each area remain open and are being actively worked on.

Prof. Dr. Oliver Stein
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (2 papers)

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Research

17 pages, 390 KiB  
Article
Finite and Symmetric Euler Sums and Finite and Symmetric (Alternating) Multiple T-Values
by Jianqiang Zhao
Axioms 2024, 13(4), 210; https://doi.org/10.3390/axioms13040210 - 23 Mar 2024
Cited by 1 | Viewed by 904
Abstract
In this paper, we will study finite multiple T-values (MTVs) and their alternating versions, which are level two and level four variations of finite multiple zeta values, respectively. We will first provide some structural results for level two finite multiple zeta values [...] Read more.
In this paper, we will study finite multiple T-values (MTVs) and their alternating versions, which are level two and level four variations of finite multiple zeta values, respectively. We will first provide some structural results for level two finite multiple zeta values (i.e., finite Euler sums) for small weights, guided by the author’s previous conjecture that the finite Euler sum space of weight, w, is isomorphic to a quotient Euler sum space of weight, w. Then, by utilizing some well-known properties of the classical alternating MTVs, we will derive a few important Q-linear relations among the finite alternating MTVs, including the reversal, linear shuffle, and sum relations. We then compute the upper bound for the dimension of the Q-span of finite (alternating) MTVs for some small weights by rigorously using the newly discovered relations, numerically aided by computers. Full article
(This article belongs to the Special Issue Advances in Number Theory and Applications)
10 pages, 281 KiB  
Article
Vanishing Property of BRST Cohomology for Modified Highest Weight Modules
by Namhee Kwon
Axioms 2023, 12(6), 550; https://doi.org/10.3390/axioms12060550 - 2 Jun 2023
Viewed by 867
Abstract
We construct certain modified highest weight modules which are called quasi highest weight modules in this paper. Using the quasi highest weight modules, we introduce a new category of modules over an affine Lie superalgebra which contains projective covers. We also prove that [...] Read more.
We construct certain modified highest weight modules which are called quasi highest weight modules in this paper. Using the quasi highest weight modules, we introduce a new category of modules over an affine Lie superalgebra which contains projective covers. We also prove that both these projective covers and the quasi highest weight modules satisfy the vanishing property of BRST cohomology. Full article
(This article belongs to the Special Issue Advances in Number Theory and Applications)
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