Values at the positive integral points of the zeta-function of the Hill operator with a finite-zone potential
Let \(L=-d^ 2/dx^ 2+g(x)\) be the Hill operator with finite-zone potential, \(S(1)=\{\lambda_ v\}\) the set of eigenvalues of the periodic boundary value problem for L, S(-1) the set of eigenvalues of the antiperiodic boundary value problem. The author gives explicit formulas for \(\zeta (k;L-w)= \sum'(\lambda_ v-w)^{-k}\) \((k=1,2,...)\), where \(w\in S(1)\cap S(-1)\) (\(\sum'\) denotes that the term with \(\lambda_ v=w\) is omitted in the case when \(w\in S(1)\).
scientific article; zbMATH DE number 3953279