Geodesic
Covariant Hyperelliptic Functions of Genus Two
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 5-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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We report results of investigations concerning the role of representations of $SL_2(\mathbb C)$ in the theory of genus-two hyperelliptic functions. We discuss the role of these representations in the classical theory as well as introduce a family of new, naturally covariant $\mathcal P$ functions.
Keywords: hyperelliptic curves, covariance, $\wp$-functions, Hirota derivatives. 
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C. Athorne. Covariant Hyperelliptic Functions of Genus Two. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 1, pp. 5-13. http://geodesic.mathdoc.fr/item/TMF_2003_137_1_a1/

[1] C. Athorne, J. J. C. Eilbeck, V. Z. Enolski, An $SL_2$ covariant theory of genus 2 hyperelliptic functions, Glasgow Dept. Math. Preprint, Glasgow Dept. Math., Glasgow, 2002 | MR

[2] C. Athorne, J. J. C. Eilbeck, V. Z. Enolski, Identities for the classical genus 2 $\wp$ function, Glasgow Dept. Math. Preprint, Glasgow Dept. Math., Glasgow, 2002 | MR

[3] H. F. Baker, Multiply Periodic Functions, Cambridge Univ. Press, Cambridge, 1907 | Zbl

[4] R. Hirota, “Direct method of finding exact solutions of nonlinear evolution equations”, Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications, Lect. Notes Math., 515, ed. R. M. Miura, Springer, Berlin, 1976, 40–68 | DOI | MR

[5] C. Athorne, Phys. Lett. A, 256 (1999), 20–24 | DOI | MR | Zbl

[6] C. Athorne, Glasgow Math. J., 2001, 1–8 | DOI | MR | Zbl

[7] B. Grammaticos, A. Ramani, J. Hietarinta, Phys. Lett. A, 190 (1994), 65–70 | DOI | MR

[8] P. J. Olver, J. A. Sanders, Adv. Appl. Math., 25 (2000), 252–283 | DOI | MR | Zbl

[9] V. M. Buchstaber, V. Z. Enolski'i, D. V. Leykin, Rev. Math. Phys., 10 (1997), 3–120 | Zbl