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Transcendental trace formulas for finite-gap potentials. (English. Russian original) Zbl 1256.81042
Theor. Math. Phys. 164, No. 1, 920-928 (2010); translation from Teor. Mat. Fiz. 164, No. 1, 108-118 (2010).
Summary: We show that formulas differing from classical analogues of rational trace formulas for algebraic-geometric potentials occur in the theory of finite-gap integration of spectral equations. The new formulas contain transcendental modular functions and hypergeometric series. They provide results in transcendental relations for theta functions.
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
33C20 Generalized hypergeometric series, \({}_pF_q\)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
11F03 Modular and automorphic functions
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