SPECIAL SOLUTIONS FOR THE LAPLACE AND DIFFUSION EQUATIONS ASSOCIATED WITH THE ALGEBRAIC NUMBER FIELD

This article is devoted to the even entire functions, which are the exact solutions for the Laplace and diffusion equations. These functions are considered in the alge-braic 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.

Automated summary

This article discusses the use of entire functions as exact solutions for the Laplace and diffusion equations, considering them in the algebraic number field. The hypothesis is that these functions have purely real zeros throughout the entire complex plane, suggesting new connections between algebraic number theory and mathematical physics.