Abelian Functions for Trigonal Curves of Genus Three
نویسندگان
چکیده
J. C. Eilbeck,1 V. Z. Enolski,2 S. Matsutani,3 Y. Ônishi4 and E. Previato5 1Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS UK, 2Institute of Magnetism, Vernadski blvd. 36, Kiev-142, Ukraine, 38-21-1 Higashi-Linkan, Sagamihara, 228-0811, Japan, 4Faculty of Humanities and Social Sciences, Iwate University, Ueda 3-18-34, Morioka 020-8550, Japan, and 5Department of Mathematics and Statistics, Boston University, Boston, MA 02215-2411, USA
منابع مشابه
Abelian Functions for Purely Trigonal Curves of Genus Three
We develop the theory of generalized Weierstrass σ and ℘ functions defined on a trigonal curve of genus three. The specific example of the “purely trigonal”curve y = x +λ3x 3 +λ2x 2 +λ1x+λ0 is discussed in detail, including a list of the associated partial differential equations satisfied by the ℘ functions, and the derivation of two addition formulae.
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We discuss the theory of generalized Weierstrass σ and ℘ functions defined on a trigonal curve of genus four, following earlier work on the genus three case. The specific example of the “purely trigonal” (or “cyclic trigonal”) curve y = x + λ4x 4 + λ3x 3 + λ2x 2 + λ1x+ λ0 is discussed in detail, including a list of some of the associated partial differential equations satisfied by the ℘ functio...
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In the theory of elliptic functions, there are two kinds of formulae of FrobeniusStickelberger [FS] and of Kiepert [K], both of which connect the function σ(u) with ℘(u) and its (higher) derivatives through determinants. These formulae are naturally generalized to hyperelliptic functions by the papers [Ô1], [Ô2], and [Ô3]. Avoiding an unneceessary generality, we restrict the story only for the ...
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