A NEW PROGRAM FOR THE ENTIRE FUNCTIONS IN NUMBER THEORY

Xiao-Jun Yang
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Xiao-Jun Yang: State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering and School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China2Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia3Department of Mathematics, College of Science, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

FRACTALS (fractals), 2024, vol. 32, issue 04, 1-12

Abstract: In this paper, we propose a new program for introducing the sign of the functional equation to present the entire functions of order one in number theory. We suggest some open problems for the zeros of these entire functions related to the completed Dedekind zeta function, completed quadratic Dirichlet L-functions, completed Ramanujan zeta function and completed automorphic L-function. These lead to the contribution to giving the deep understanding for diffusion equations associated with the entire functions of order one in number theory.

Keywords: Entire Function; Diffusion Equation; Completed Dedekind Zeta Function; Completed Quadratic Dirichlet L-Functions; Completed Ramanujan Zeta Function; Completed Automorphic L-Function (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X23401229

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