The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations
Shigeki Matsutani
Gebundenes Buch

The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations

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This book's area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics. Special functions such as elliptic or automorphic functions have an algebro-geometric nature. These attributes permeate the book. The "Kleinian sigma function", or "higher-genus Weierstrass sigma function" generalizes the elliptic sigma function. It appears for the first time in the work of Weierstrass. Klein gave an explicit definition for hyperelliptic or genus-three curves, as a modular invariant analogue of the Riemann theta function on the Jacobian (the t...