Abstract
In this article, we use results of Number Theory to prove the conjecture on the eigenvalue problem of a 2D elliptic PDE proposed by P.Korman in his recent paper \cite{ref}: for any even integer $2k$, one can find an eigenvalue $N$ that can be represented as $N=a^{2}+b^{2}$, with integers $a\neq b$ with multiplicity $2k$, while for any odd integer $2k + 1$, one can find an integer $M$ that can be represented as $M=a^{2}+b^{2}$ with $a\neq b$ and multiplicity $2k+1$. In addition, the manuscript gives the formula to find those $N$'s.
Faculty Sponsor
Taige Wang
Recommended Citation
Zhou, Changfeng
(2025)
"Multiplicity Of Laplacian Eigenvalues That Can Be Represented By Sum Of Two Squares Using Number Theory,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 26:
Iss.
2, Article 2.
Available at:
https://scholar.rose-hulman.edu/rhumj/vol26/iss2/2