Geodesic
Solution of functional equations related to elliptic functions
Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 105-117.

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

Functional equations of the form $f(x+y) g(x-y) = \sum _{j=1}^n \alpha _j(x)\beta _j(y)$ as well as of the form $f_1(x+z) f_2(y+z) f_3(x+y-z) = \sum _{j=1}^{m} \phi _j(x,y) \psi _j(z)$ are solved for unknown entire functions $f,g,\alpha _j,\beta _j: \mathbb{C} \to \mathbb{C} $ and $f_1,f_2,f_3,\psi _j: \mathbb{C} \to \mathbb{C} $, $\phi _j: \mathbb{C} ^2\to \mathbb{C} $ in the cases of $n=3$ and $m=4$. 
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     author = {A. A. Illarionov},
     title = {Solution of functional equations related to elliptic functions},
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}
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A. A. Illarionov. Solution of functional equations related to elliptic functions. Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 105-117. http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a5/

[1] Bonk M., “The addition theorem of Weierstrass's sigma function”, Math. Ann., 298 (1994), 591–610 | DOI | MR | Zbl

[2] Bonk M., “The characterization of theta functions by functional equations”, Abh. Math. Semin. Univ. Hamburg, 65 (1995), 29–55 | DOI | MR | Zbl

[3] Bonk M., “The addition formula for theta functions”, Aequationes math., 53:1–2 (1997), 54–72 | DOI | MR | Zbl

[4] V. M. Buchstaber, I. M. Krichever, “Integrable equations, addition theorems, and the Riemann–Schottky problem”, Russ. Math. Surv., 61 (2006), 19–78 | DOI | DOI | MR | Zbl

[5] V. M. Buchstaber, D. V. Leikin, “Trilinear functional equations”, Russ. Math. Surv., 60 (2005), 341–343 | DOI | DOI | MR | Zbl

[6] V. M. Buchstaber, D. V. Leikin, “Addition laws on Jacobian varieties of plane algebraic curves”, Proc. Steklov Inst. Math., 251 (2005), 49–120 | MR | Zbl

[7] V. A. Bykovskii, “Hyperquasipolynomials and their applications”, Funct. Anal. Appl., 50 (2016), 193–203 | DOI | DOI | MR | Zbl

[8] A. A. Illarionov, “Functional equations and Weierstrass sigma-functions”, Funct. Anal. Appl., 50 (2016), 281–290 | DOI | DOI | MR | Zbl

[9] A. A. Illarionov, “Solution of a functional equation concerning trilinear differential operators”, Dal'nevost. Mat. Zh., 16:2 (2016), 169–180 | MR | Zbl

[10] Janson S., Peetre J., Wallstén R., “A new look on Hankel forms over Fock space”, Stud. math., 95:1 (1989), 33–41 | DOI | MR | Zbl

[11] Járai A., Sander W., “On the characterization of Weierstrass's sigma function”, Functional equations—results and advances, Adv. Math., 3, Kluwer, Dordrecht, 2002, 29–79 | MR | Zbl

[12] Levi-Civita T., “Sulle funzioni che ammettono una formula d'addizione del tipo $f(x+y) = \sum _{i=1}^n X_i(x) Y_i(y)$”, Rom. Accad. Lincei. Rend. Ser. 5, 22:2 (1913), 181–183 | Zbl

[13] D. Mumford, Tata Lectures on Theta, v. I, Birkhäuser, Boston, 1983 | MR | MR | Zbl

[14] Peano G., “Sur le déterminant wronskien”, Mathesis, 9 (1889), 110–112

[15] Rochberg R., Rubel L.A., “A functional equation”, Indiana Univ. Math. J., 41:2 (1992), 363–376 | DOI | MR | Zbl

[16] S. Stoilow, Notiuni si principii fundamentale, v. 1, Ed. Acad. Repub. Populare Rom., Bucuresti, 1954 | MR

[17] E. T. Whittaker, G. N. Watson, A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions, Univ. Press, Cambridge, 1927 | MR | Zbl