Explicit Formulas for Differentiation of Hyperelliptic Functions
Matematičeskie zametki, Tome 114 (2023) no. 6, pp. 808-821.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper provides an explicit solution to the well-known problem of differentiation of hyperelliptic functions with respect to parameters of the corresponding hyperelliptic curve.
Keywords: sigma function, generators of the field of hyperelliptic functions, heat equation, Schrödinger equation, nonholonomic frame, Lie algebra of differential operators.
@article{MZM_2023_114_6_a1,
     author = {E. Yu. Bunkova and V. M. Buchstaber},
     title = {Explicit {Formulas} for {Differentiation} of {Hyperelliptic} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {808--821},
     publisher = {mathdoc},
     volume = {114},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_6_a1/}
}
TY  - JOUR
AU  - E. Yu. Bunkova
AU  - V. M. Buchstaber
TI  - Explicit Formulas for Differentiation of Hyperelliptic Functions
JO  - Matematičeskie zametki
PY  - 2023
SP  - 808
EP  - 821
VL  - 114
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_114_6_a1/
LA  - ru
ID  - MZM_2023_114_6_a1
ER  - 
%0 Journal Article
%A E. Yu. Bunkova
%A V. M. Buchstaber
%T Explicit Formulas for Differentiation of Hyperelliptic Functions
%J Matematičeskie zametki
%D 2023
%P 808-821
%V 114
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2023_114_6_a1/
%G ru
%F MZM_2023_114_6_a1
E. Yu. Bunkova; V. M. Buchstaber. Explicit Formulas for Differentiation of Hyperelliptic Functions. Matematičeskie zametki, Tome 114 (2023) no. 6, pp. 808-821. http://geodesic.mathdoc.fr/item/MZM_2023_114_6_a1/

[1] F. G. Frobenius, L. Stickelberger, “Über die Differentiation der elliptischen Functionen nach den Perioden und Invarianten”, J. Reine Angew. Math., 92 (1882), 311–337 | MR

[2] B. A. Dubrovin, V. B. Matveev, S. P. Novikov, “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, UMN, 31:1 (187) (1976), 55–136 | MR | Zbl

[3] I. M. Krichever, “Metody algebraicheskoi geometrii v teorii nelineinykh uravnenii”, UMN, 32:6 (198) (1977), 183–208 | MR | Zbl

[4] B. A. Dubrovin, “Teta-funktsii i nelineinye uravneniya”, UMN, 36:2 (218) (1981), 11–80 | MR | Zbl

[5] V. M. Bukhshtaber, D. V. Leikin, “Reshenie zadachi differentsirovaniya abelevykh funktsii po parametram dlya semeistv $(n,s)$-krivykh”, Funkts. analiz i ego pril., 42:4 (2008), 24–36 | DOI | MR | Zbl

[6] V. M. Buchstaber, V. Z. Enolski, D. V. Leykin, “$\sigma$-Functions: old and new results”, Integrable Systems and Algebraic Geometry, v. 2, London Math. Soc. Lecture Note Ser., 459, Cambridge Univ. Press, Cambridge, 2020, 175–214 | MR

[7] F. Klein, “Ueber hyperelliptische Sigmafunctionen”, Math. Ann., 27:3 (1886), 431–464 | DOI | MR

[8] F. Klein, “Ueber hyperelliptische Sigmafunctionen”, Math. Ann., 32:3 (1888), 351–380 | DOI | MR

[9] H. F. Baker, “On the hyperelliptic sigma functions”, Amer. J. Math., 20:4 (1898), 301–384 | DOI | MR

[10] V. M. Buchstaber, V. Z. Enolskii, D. V. Leikin, “Hyperelliptic Kleinian functions and applications”, Solitons, Geometry, and Topology: On the Crossroad, Amer. Math. Soc. Transl. Ser. 2, 179, Amer. Math. Soc., Providence, RI, 1997, 1–34 | MR

[11] V. M. Buchstaber, V. Z. Enolskii, D. V. Leikin, “Kleinian functions, hyperelliptic Jacobians and applications”, Reviews in Mathematics and Math. Physics, Gordon and Breach, London, 1997, 3–120

[12] V. M. Buchstaber, V. Z. Enolskii, D. V. Leikin, Multi-Dimensional Sigma-Functions, arXiv: 1208.0990

[13] B. A. Dubrovin, “Geometry of 2D topological field theories”, Integrable Systems and Quantum Groups (Montecatini Terme, 1993), Lecture Notes in Math., 1620, Springer-Verlag, Berlin, 1994, 120–348 | DOI | MR

[14] V. M. Bukhshtaber, “Polinomialnye dinamicheskie sistemy i uravnenie Kortevega–de Friza”, Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Trudy MIAN, 294, Nauka, M., 2016, 191–215 | DOI | MR

[15] E. Yu. Bunkova, “Differentiation of genus 3 hyperelliptic functions”, European Journal of Mathematics, 4:1 (2018), 93–112 | DOI | MR

[16] V. M. Bukhshtaber, E. Yu. Bunkova, “Sigma-funktsii i algebry Li operatorov Shredingera”, Funkts. analiz i ego pril., 54:4 (2020), 3–16 | DOI | MR

[17] V. M. Bukhshtaber, D. V. Leikin, “Polinomialnye algebry Li”, Funkts. analiz i ego pril., 36:4 (2002), 18–34 | DOI | MR | Zbl

[18] V. I. Arnold, Singularities of Caustics and Wave Fronts, Math. Appl. (Soviet Ser.), 62, Kluwer Acad., Dordrecht, 1990 | DOI | MR

[19] V. M. Bukhshtaber, D. V. Leikin, “Uravneniya teploprovodnosti v negolonomnom repere”, Funkts. analiz i ego pril., 38:2 (2004), 12–27 | DOI | MR | Zbl

[20] V. M. Bukhshtaber, E. Yu. Bunkova, “Algebry Li operatorov teploprovodnosti v negolonomnom repere”, Matem. zametki, 108:1 (2020), 17–32 | DOI | MR

[21] V. M. Bukhshtaber, E. Yu. Bunkova, “Giperellipticheskie sigma-funktsii i polinomy Adlera–Mozera”, Funkts. analiz i ego pril., 55:3 (2021), 3–25 | DOI

[22] V. M. Bukhshtaber, E. Yu. Bunkova, “Parametricheskaya ierarkhiya Kortevega–de Friza i giperellipticheskie sigma-funktsii”, Funkts. analiz i ego pril., 56:3 (2022), 16–38 | DOI | MR

[23] V. M. Buchstaber, S. Yu. Shorina, “The $w$-function of the KdV hierarchy”, Geometry, Topology, and Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, 212, Amer. Math. Soc., Providence, RI, 2004, 41–66 | MR

[24] N. A. Kudryashov, Analiticheskaya teoriya nelineinykh differentsialnykh uravnenii, RKhD, M.–Izhevsk, 2004