ON A TEMPERED XI FUNCTION ASSOCIATED WITH THE RIEMANN XI FUNCTION

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, 1-5

Abstract: In this paper, we propose a tempered xi function obtained by the recombination of the decomposable functions for the Riemann xi function for the first time. We first obtain its functional equation and series representation. We then suggest three equivalent open problems for the zeros for it. We finally consider its behaviors on the critical line.

Keywords: Tempered Xi Function; Riemann Xi Function; Functional Equation; Series Representation; Nontrivial Zeros; Critical Line (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X23401163

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