Geodesic
Transcendental trace formulas for finite-gap potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 1, pp. 108-118

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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 result in transcendental relations for theta functions.
Keywords: spectral problem, finite-gap potential, modular function.
Mots-clés : trace formula 
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     author = {Yu. V. Brezhnev},
     title = {Transcendental trace formulas for finite-gap potentials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_1_a6/}
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Yu. V. Brezhnev. Transcendental trace formulas for finite-gap potentials. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 1, pp. 108-118. http://geodesic.mathdoc.fr/item/TMF_2010_164_1_a6/