Applications of Number Theory to Science and Technology

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 August 2023) | Viewed by 1086

Special Issue Editors


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Guest Editor
Department of Mathematics, School of Science and Technology, University of Trás-os-Montes e Alto Douro, Vila Real, Portugal
Interests: number theory; numerical sequences; cryptography; recurrence relations
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Engineering, School of Science and Technology, University of Trás-os-Montes e Alto Douro, Vila Real, Portugal
Interests: computer vision; machine learning; animal and human movement analysis
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Mathematics, School of Science and Technology, University of Trás-os-Montes e Alto Douro, Vila Real, Portugal
Interests: number theory; numerical sequences; recurrence relations

Special Issue Information

Dear Colleagues,

Number theory is a branch of mathematics that involves the study of number properties, giving special attention to integers. Today, number theory is one of the most dynamic areas of research with several applications, for instance, in cryptography, websites for e-commerce, coding, data security, in the design and analysis of computer hardware, in the study of communication and information theory, in the study of complexity theory, among others.

The purpose of this Special Issue is to reveal the most varied applications of number theory in most fields of science and technology. In particular, applications of certain numerical sequences are also welcome.

Contributions of high-quality papers that outline the current trends and activities in modern number theory are welcome. The topics of interest for this Special Issue include, but are not limited to, modular forms, hypergeometric functions, elliptic curves, Galois theory, special numbers, special functions, the distribution of prime numbers, Diophantine equations, L-functions, and Diophantine approximation.

If you are working in pure or applied number theory with applications in various fields of science and technology—for instance, in cryptography, computer animation, machine translation and other fields—please submit a paper with this focus and scope.

Dr. Paula M. C. Catarino
Dr. Vitor Filipe
Dr. Paulo Vasco
Guest Editors

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.

Keywords

  • number theory
  • encryption
  • algorithm
  • prime numbers
  • cryptography
  • numerical sequences

Published Papers (1 paper)

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Research

24 pages, 415 KiB  
Article
Infinite Series Concerning Tails of Riemann Zeta Values
by Chunli Li and Wenchang Chu
Axioms 2023, 12(8), 761; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms12080761 - 02 Aug 2023
Viewed by 590
Abstract
Infinite series involving Riemann’s zeta and Dirichlet’s lambda tails, and weighted by three harmonic-like elementary symmetric functions are examined. By means of integral representations of zeta tails together with the telescopic approach, twelve general summation theorems are established that express these series as [...] Read more.
Infinite series involving Riemann’s zeta and Dirichlet’s lambda tails, and weighted by three harmonic-like elementary symmetric functions are examined. By means of integral representations of zeta tails together with the telescopic approach, twelve general summation theorems are established that express these series as coefficients of the bivariate beta function Beta(u,v). By further expanding Beta(u,v) into Laurent series in u and v, several explicit summation formulae are shown as consequences. Full article
(This article belongs to the Special Issue Applications of Number Theory to Science and Technology)
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