Eigenvalues of a Differential Operator and Zeros of the Riemann $ζ$-Function (Analysis in Theory and Applications, 2021)
The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $ζ$-function. Moreover, their corresponding multiplicities are the same.
Keywords: Hilbert-Pόlya space; zeros of zeta function; differential operator; eigenvalue.