THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

Authors of this Paper

External Links

online first only

Novel solutions for the heat equations arising in the elliptic curves over the field of rational numbers

ABSTRACT
In this article we consider the solutions of the heat equations with use of the elliptic curves over the field of rational numbers. We propose the entire functions associated with the Hasse-Weil L-function. We show the conjectures that new functions have only real zeros in the entire function plane. The obtained results are proposed as new tool to describe the complex behaviors of the heat problems as well as number theory.
KEYWORDS
PAPER SUBMITTED: 2022-08-07
PAPER REVISED: 2022-11-12
PAPER ACCEPTED: 2022-11-22
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI220807001Y
REFERENCES
  1. Silverman, J. H., The Arithmetic of Elliptic Curves, Springer, New York, 2009
  2. Diamond, F., and Shurman, J. M., A First Course in Modular Forms, Springer, New York, 2005
  3. Breuil, C., et al., On the Modularity of Elliptic Curves over Q: Wild 3-adic Exercises, Journal of the American Mathematical Society, 14 (2001), 4, pp.843-939
  4. Wiles, A., Modular Elliptic Curves and Fermat's Last Theorem, Annals of mathematics, 141 (1995), 3, pp.443-551
  5. Taylor, R. and Wiles, A., Ring-theoretic Properties of Certain Hecke Algebras, Annals of Mathematics, 141 (1995), 3, pp.553-572
  6. Yang, X. J., Theory and Applications of Special Functions for Scientists and Engineers, Springer Singapore, 2021
  7. Cremona, J. E., Algorithms for Modular Elliptic Curves, Cambridge University Press, Cambridge, 1997
  8. Cannon, J. R., The One-dimensional Heat Equation, Vol. 23, Cambridge University Press, Cambridge, 1984
  9. Ogg, A., Modular Forms and Dirichlet Series, Vol. 39, WA Benjamin, New York, 1969
  10. Boas, R. P., Entire Functions, Academic Press, New York, USA, 1954