Thermal Science 2023 Volume 27, Issue 1 Part B, Pages: 439-446
https://doi.org/10.2298/TSCI220807001Y
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Novel solutions for the heat equations arising in the elliptic curves over the field of rational numbers
Yang Xiao-Jun (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, Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea), dyangxiaojun@163.com
Cui Ping (School of Mathematics and Statistics, Qujing Normal University, Qujing , Yunnan, China)
Xu Feng (Business School, Suzhou Vocational University, Suzhou , Jiangsu, China)
In this article we consider the solutions of the heat equations with use of the elliptic curves over the field of rational numbers. We propose the entire functions associated with the Hasse-Weil L-function. We show the conjectures that new functions have only real zeros in the entire function plane. The obtained results are proposed as new tool to describe the complex behaviors of the heat problems as well as number theory.
Keywords: heat equation, solution, Hasse-Weil L-function, elliptic curves, entire functions, number theory
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