Abelian Function
المؤلف:
Baker, H. F.
المصدر:
An Introduction to the Theory of Multiply Periodic Functions. London: Cambridge University Press, 1907.
الجزء والصفحة:
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22-4-2019
1960
Abelian Function
An inverse function of an Abelian integral. Abelian functions have two variables and four periods, and can be defined by
(Baker 1907, p. 21). Abelian functions are a generalization of elliptic functions, and are also called hyperelliptic functions.
Any Abelian function can be expressed as a ratio of homogeneous polynomials of the Riemann theta function (Igusa 1972, Deconinck et al. 2004).
REFERENCES:
Baker, H. F. An Introduction to the Theory of Multiply Periodic Functions. London: Cambridge University Press, 1907.
Baker, H. F. Abelian Functions: Abel's Theorem and the Allied Theory, Including the Theory of the Theta Functions. New York: Cambridge University Press, 1995.
Deconinck, B.; Heil, M.; Bobenko, A.; van Hoeij, M.; and Schmies, M. "Computing Riemann Theta Functions." Math. Comput. 73, 1417-1442, 2004.
Igusa, J.-I. Theta Functions. New York: Springer-Verlag, 1972.
Weisstein, E. W. "Books about Abelian Functions." http://www.ericweisstein.com/encyclopedias/books/AbelianFunctions.html.
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