THERMAL SCIENCE

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An even entire function of order one is a special solution for a classical wave equation in one-dimensional space

ABSTRACT
In this article we consider an even entire function of order one as the solution of the classical wave equation in one-dimensional space. We suggest a conjecture that this function has only purely real zeros in the entire complex plane. This is given as a new prospective on a nice connection with number theory and wave equation.
KEYWORDS
PAPER SUBMITTED: 2022-11-11
PAPER REVISED: 2022-12-15
PAPER ACCEPTED: 2022-12-17
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI221111008Y
REFERENCES
  1. De Bruijn, N. G., The roots of trigonometric integrals, Duke Mathematical Journal, 17(1950), 3, pp.197-226
  2. Newman, C. M., Fourier transforms with only real zeros, Proceedings of the American Mathematical Society, 61 (1976), 2, pp.245-251
  3. Jensen, J. L., Recherches sur la théorie des équations, Acta Mathematica, 36(1913), 1, pp.181-195
  4. Riemann, G. F. B., Über die Anzahl der Primzahlen unter einer gegebenen Grösse, Monatsberichte der Berliner Akademie, 2 (1859), November, pp.671-680
  5. Edwards, H. M., Riemanns'Zeta Function, Academic press, New York, 1974
  6. Yang, X. J., Theory and Applications of Special Functions for Scientists and Engineers, Springer Singapore, 2021
  7. Balazs, N. L., On the solution of the wave equation with moving boundaries, Journal of Mathematical Analysis and Applications, 3(1961), 3, pp.472-484
  8. Wintner, A., A note on the Riemann ξ-function, Journal of the London Mathematical Society, 1(1935), 2, pp.82-83
  9. Boas, R. P., Entire Functions, Academic Press, New York, USA, 1954