Geodesic
Transcendental trace formulas for finite-gap potentials
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 1, pp. 108-118 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] L. A. Dickey, Solitons Equations and Hamiltonian Systems, Adv. Ser. Math. Phys., 26, World Sci., Singapore, 2003 | DOI | MR | Zbl

[2] M. Błaszak, Multi-Hamiltonian Theory of Dynamical Systems, Texts Monogr. Phys., Springer, Berlin, 1998 | MR | Zbl

[3] Yu. V. Brezhnev, UMN, 57:2(344) (2002), 191–192 | DOI | MR | Zbl

[4] V. M. Bukhshtaber, D. V. Leikin, V. Z. Enolskii, Funkts. analiz i ego pril., 34:3 (2000), 1–16 | DOI | MR | Zbl

[5] D. J. Kaup, Stud. Appl. Math., 62:3 (1980), 189–216 | DOI | MR | Zbl

[6] D. Koks, Dzh. Littl, D. O'Shi, Idealy, mnogoobraziya i algoritmy, Mir, M., 2000 | MR | Zbl

[7] N. I. Akhiezer, Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR | Zbl

[8] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. Ellipticheskie i avtomorfnye funktsii. Funktsii Lame i Mate, Spravochnaya matematicheskaya biblioteka, Nauka, M., 1967 | MR | MR | Zbl

[9] I. M. Vinogradov (red.), Matematicheskaya entsiklopediya, v. III, Sovetskaya entsiklopediya, M., 1982 | MR | Zbl

[10] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. I, Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Nauka, M., 1973 | MR | MR | Zbl

[11] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza, ch. 2, Fizmatlit, M., 1963 | MR | Zbl

[12] D. Mamford, Lektsii o teta-funktsiyakh, Mir, M., 1988 | MR | MR