Far Eastern Mathematical Journal

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An arithmetic interpretation of a three-term identity from the theta functions theory

M. D. Monina

2014, issue 2, P. 242–247

Abstract

The article offers the proof of a three-term identity from the theta functions theory, based on Liouville's arithmetical methods.

Keywords: elliptic function, theta function, Liouville's methods, three-term identity

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References

[1] K. Weierstra\ss, Math. Werke, Bd. 5, Berlin, 1915. [2] J. V. Uspensky, M. A. Heaslet, Elementary Number Theory, McGraw-Hill Book Company, Inc., New York and London, 1939. [3] B. A. Venkov, E'lementarnaya teoriya chisel, ONTI NKTP SSSR, M.; Leningrad, 1937. [4] Kenneth S. Williams, Number theory in the spirit of Liouville, London Mathematical Society Student Texts, 76, Cambridge University Press, 2011. [5] N. V. Budarina, V. A. Bykovskij, “Arifmeticheskaya priroda tozhdesv dlya trojnogo i pyatikratnogo proizvedenij”, Dal'nevostochnyj matematicheskij zhurnal, 11:2 (2011), 140–148. [6] V. A. Bykovskij, M. D. Monina, “Arifmeticheskie tozhdestva, associirovannye s kvadratichnymi formami, i ix prilozheniya”, Doklady Akademii nauk, 449:5 (2013), 503–506. [7] V. A. Bykovskij, M. D. Monina, “Ob arifmeticheskoj prirode nekotoryx tozhdestv teorii e'llipticheskix funkcij”, Dal'nevostochnyj matematicheskij zhurnal, 13:1 (2013), 15–34.

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