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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.
##### MSC:
 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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