THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Xiao-Jun Yang

,

Ahmed Alshehri

,

Ping Cui

THE METHOD FOR THE HEAT-DIFFUSION EQUATION IN ANALYTIC NUMBER THEORY

ABSTRACT
This paper addresses the entire functions via theory of the tempered xi function. The zeros of the entire functions by the Fourier sine and cosine integrals are stud­ied in detail. The method for the heat-diffusion equation is proposed to structure the connection between Fourier analysis and heat-diffusion equation show the open problems in analytic number theory.
KEYWORDS
tempered xi function, Fourier analysis, heat-diffusion equation, open problems, analytic number theory
PAPER SUBMITTED: 2023-03-13
PAPER REVISED: 2023-05-14
PAPER ACCEPTED: 2023-06-19
PUBLISHED ONLINE: 2023-11-05
DOI REFERENCE: https://doi.org/10.2298/TSCI2305837Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 5, PAGES [3837 - 3844]
REFERENCES
  1. Yang, X. J., On a Tempered Xi Function Associated with the Riemann Xi Function, Fractals, On-line first, doi.org/10.1142/S0218348X23401163, 2023
  2. ***, www.worldscientific.com/pb-assets/wspcsite/journals/fractals-challenge-1685316817370.pdf
  3. Yang, X. J., A New Program for the Entire Functions in Number Theory, Fractals, On-line first, doi.org:10.1142/S0218348X23401229, 2023
  4. Yang, X. J., et al., A New Odd Entire Function of Order One Arising in the Heat Problem, Thermal Science, 27 (2023), 1B, pp. 505-512
  5. Riemann, B., Ueber die Anzahl der Primzahlen unter einer gegebenen Grosse (in German), Monatsberichte der Berliner Akademie, Berlin, Germany, 1859, pp. 671-680
  6. Edwards, H. M., Riemann's Zeta Function, Courier Corporation, Chelmsford, Mass., USA, 2001, Vol. 58
  7. Titchmarsh, E. C., The Theory of the Riemann Zeta-Function, (Heath-Brown, D. R. ed.), Oxford University Press, Oxford, UK, 1986
  8. Jensen, J. L. W. V., Recherches sur la théorie des équations (in French), Acta Mathematics, 36 (1913), 1, pp. 181-195
  9. Yang, X. J., Fan, Y. R., The Series Representations for the J and H Functions Applied in the Heat-Diffusion Equation, Thermal Science, 25 (2021), 6B, pp. 4631-4642
PDF VERSION [DOWNLOAD]
The method for the heat-diffusion equation in analytic number theory

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence