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TMF, 2010, Volume 164, Number 1, Pages 108–118 (Mi tmf6527)  

This article is cited in 1 scientific paper (total in 1 paper)

Transcendental trace formulas for finite-gap potentials

Yu. V. Brezhnev

Tomsk State University, Tomsk, Russia

Abstract: 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, trace formula, modular function

DOI: https://doi.org/10.4213/tmf6527

Full text: PDF file (429 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 164:1, 920–928

Bibliographic databases:

Received: 16.12.2009

Citation: Yu. V. Brezhnev, “Transcendental trace formulas for finite-gap potentials”, TMF, 164:1 (2010), 108–118; Theoret. and Math. Phys., 164:1 (2010), 920–928

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Brezhnev Yu.V., “Non-Canonical Extension of Theta-Functions and Modular Integrability of Theta-Constants”, Proc. R. Soc. Edinb. Sect. A-Math., 143:4 (2013), 689–738  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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