Special solutions for the Laplace and diffusion equations associated with the algebraic number field-Reference-Cited by-同舟云学术

Special solutions for the Laplace and diffusion equations associated with the algebraic number field

Published:2023 Issue:1 Part B Volume:27 Page:477-481
ISSN:0354-9836
Container-title:Thermal Science
language:en
Short-container-title:THERM SCI

Author:

Yang Xiao-Jun¹,Sweilam Nasser²,Bayram Mustafa³

Affiliation:

1. State Key Laboratory for Geo-Mechanics and Deep Underground Engineering, and School of Mathematics, China University of Mining and Technology, Xuzhou, China + Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia + Department of Mathematics, College of Science, Kyung Hee University, Seoul, Republic of Korea

2. Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt

3. Computer Engineering Department, Faculty of Engineering and Natural Sciences, Biruni University, Istanbul, Turkey

Abstract

This article is devoted to the even entire functions, which are the exact solutions for the Laplace and diffusion equations. These functions are considered in the algebraic number field. We guess that the functions have purely real zeros in the entire complex plane. These are proposed as new connections with algebraic number theory and mathematical physics.

Publisher

National Library of Serbia

Subject

Renewable Energy, Sustainability and the Environment

Reference6 articles.

1. Dedekind, R., Über die Anzahl der Ideal-Klassen in den Verschiedenen Ordnungen Eines Endlichen Körpers, 1877, in: Gesammelte mathematische Werke, Bände I-III, Herausgegeben von Robert Fricke (in German), Emmy Noether und Öystein Ore Chelsea Publishing Co., New York, USA, 1968

2. Li, X. J., A Formula for the Dedekind ξ-function of an Imaginary Quadratic Field, Journal of Mathematical Analysis and Applications, 260 (2001), 2, pp. 404-420

3. Coffey, M. W., Toward Verification of the Riemann Hypothesis: Application of the Li Criterion, Mathematical Physics, Analysis and Geometry, 8 (2005), 3, pp. 211-255

4. Yang, X.-J., A New Even Entire Function and the Extended Riemann Hypothesis, On-line first, https://doi.org/10.48550/arXiv.1811.02418

5. Qian, Z., et al., Two Regularization Methods for a Cauchy Problem for the Laplace Equation, Journal of Mathematical Analysis and Applications, 338 (2008), 1, pp. 479-489