THERMAL SCIENCE

International Scientific Journal

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Special solutions for the Laplace and diffusion equations associated with the algebraic number field

ABSTRACT
This article is devoted to the even entire functions, which are the exact solution for the Laplace and diffusion equations. These functions are considered in the algebraic number field. We guess that the functions have purely real zeros in the entire complex plane. These are proposed as new connections with algebraic number theory and mathematical physics
KEYWORDS
PAPER SUBMITTED: 2022-11-13
PAPER REVISED: 2022-12-14
PAPER ACCEPTED: 2022-12-19
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI221113006Y
REFERENCES
  1. Dedekind, R., Über die Anzahl der Ideal-Klassen in den Verschiedenen Ordnungen Eines Endlichen Körpers, 1877, in: Gesammelte mathematische Werke, Bände I-III, Herausgegeben von Robert Fricke, Emmy Noether und öystein Ore Chelsea Publishing Co., New York, 1968
  2. Li, X. J., A Formula for the Dedekind ξ-function of an Imaginary Quadratic Field, Journal of Mathematical Analysis and Applications, 260 (2001), 2, pp.404-420
  3. Coffey, M. W., Toward Verification of the Riemann Hypothesis: Application of the Li Criterion, Mathematical Physics, Analysis and Geometry, 8 (2005), 3, pp.211-255
  4. Yang, X.-J., A New Even Entire Function and the Extended Riemann Hypothesis, doi.org/10.48550/arXiv.1811.02418
  5. Qian, Z., Fu, C. L., and Li, Z. P., Two Regularization Methods for a Cauchy Problem for the Laplace Equation, Journal of Mathematical Analysis and Applications, 338(2008), 1, pp.479-489
  6. Cannon, J. R., Esteva S. P., and Van Der Hoek, J., A Galerkin procedure for the diffusion equation subject to the specification of mass, SIAM Journal on Numerical Analysis, 24(1987), 3, pp.499-515