THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Xiao-Jun Yang

,

Mahmoud Abdel-Aty

,

Lu-Lu Geng

A NEW ODD ENTIRE FUNCTION OF ORDER ONE ARISING IN THE HEAT PROBLEM

ABSTRACT
In this article we suggest a new odd entire function of order one. We discover that it is the solution of the heat equation. We propose a new conjecture that this function has only real zeros. The obtained result gives a connection with the heat problem and number theory.
KEYWORDS
heat equation, odd entire function, heat equation, real zeros, number theory
PAPER SUBMITTED: 2022-11-05
PAPER REVISED: 2022-12-20
PAPER ACCEPTED: 2022-12-27
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI221105010Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 1, PAGES [505 - 512]
REFERENCES
  1. Riemann, G. F. B., Über die Anzahl der Primzahlen unter einer gegebenen Grösse (in German), Monats­berichte der Berliner Akademie, 2 (1859), Nov., pp. 671-680
  2. Edwards, H. M., Riemanns'Zeta Function, Academic press, New York, USA, 1974
  3. Jensen, J. L., Recherches sur la théorie des équations (in French), Acta Mathematica, 36 (1913), 1, pp. 181-195
  4. Titchmarsh, E. C., The Theory of the Riemann Zeta-function, Oxford University Press, Oxford, UK, 1986
  5. De Bruijn, N. G., The Roots of Trigonometric Integrals, Duke Mathematical Journal, 17 (1950), 3, pp. 197-226
  6. Newman, C. M., Fourier Transforms with Only Real Zeros, Proceedings of the American Mathematical Society, 61 (1976), 2, pp. 245-251
  7. Csordas, G., et al., Lehmer Pairs of Zeros, the de Bruijn-Newman Constant Λ, and the Riemann Hypoth­esis, Constructive Approximation, 10 (1994), 1, pp. 107-129
  8. Yang, X. J., On a Tempered Xi Function Associated with the Riemann Xi Function, Fractals, Accepted, 2022
  9. Cannon-, J. R., The 1-D Heat Equation, Cambridge University Press, Cambridge, UK, 1984, Vol. 23
  10. Csordas, G., et al., A Low Bound for the de Bruijn-Newman Constant Λ, Numerische Mathematik, 52 (1987), 5, pp. 483-497
  11. Boas, R. P., Entire Functions, Academic Press, New York, USA, 1954
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A new odd entire function of order one arising in the heat problem

© 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