2018/07/30 by Boris Dubrovin, Dubrovin, Boris
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Nonlinear Waves and Solitons #math-ph #math.AG #math.MP #msc:14K25
paper · pdf · doi:10.48550/arxiv.1807.11258
42 pages
arxiv created 2018/07/30 · arxiv updated 2018/07/31
Let W(z) be a n× n matrix polynomial with rational coefficients. Denote C the spectral curve det ( w⋅\bf 1-W(z)) =0. Under some natural assumptions about the structure of W(z) we prove that certain combinations of logarithmic derivatives of the Riemann theta-function of C of an arbitrary order starting from the third one all take rational values at the point of the Jacobi variety J(C) specified by the line bundle of eigenvectors of W(z).