Transcendental Trace Formulas For Finite-Gap Potentials

Details Transcendental Trace Formulas For Finite-Gap Potentials Transcendental Trace Formulas For Finite-Gap Potentials

2012-01-13

arxiv.org/abs/1201.2826v1

Theor. Math. Phys. v.164(1) (2010), 920--928

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Final version; 9 pages, LaTeX

Scientific paper

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.

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