Far Eastern Mathematical Journal

To content of the issue


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


Monina M. D.

2014, issue 1, Ń. 66-72


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

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

Download the article (PDF-file)

References

1] A. Hurwitz, ''Uber die Weierstrass'sche $\sigma$-Funktion", In Festschrift fur H.A. Schwarz, Ges. Abh. Bd. 3, pp.722-730, Berlin, 1914, 133-141.
[2] E.T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza. T. 2, Gos. izd. fiz.-mat. lit., Moskva, 1963.
[3] A. E. Polishchuk, Abelevy mnogoobraziia, teta-funktsii i preobrazovanie Fur'e, MTs-NMO, Moskva, 2010.
[4] J. V. Uspensky, M. A. Heaslet, Elementary Number Theory, McGraw-Hill Book Company, Inc., New York and London, 1939.
[5] B. A. Venkov, Elementarnaia teoriia chisel, ONTI NKTP SSSR, M.; Leningrad, 1937.
[6] Kenneth S. Williams, Number theory in the spirit of Liouville, London Mathematical Society Student Texts, 76, Cambridge University Press, 2011.
[7] N. V. Budarina, V. A. Bykovskii, “Arifmeticheskaia priroda tozhdesv dlia troinogo i piatikratnogo proizvedenii”, Dal'nevostochnyi matematicheskii zhurnal, 11:2 (2011), 140–148.
[8] V. A. Bykovskii, M. D. Monina, “Arifmeticheskie tozhdestva, assotsiirovannye s kvadratichnymi formami, i ikh prilozheniia”, Doklady Akademii nauk, 449:5 (2013), 503–506.
[9] V. A. Bykovskii, M. D. Monina, “Ob arifmeticheskoi prirode nekotorykh tozhdestv teorii ellipticheskikh funktsii”, Dal'nevostochnyi matematicheskii zhurnal, 13:1 (2013), 15–34.
[10] V. A. Bykovskii, Moduli Eikhlera-Shimury, Preprint DVO RAN. Khabarovskoe otdelenie Instituta prikladnoi matematiki, Dal'nauka, Vladivostok, 2001.
[11] V. A. Bykovskii, “Obobshchenie arifmeticheskikh tozhdestv Liuvillia i Skoruppy”, Doklady Akademii nauk, 432:6 (2010), 736–737.
[12] J. G. Huard, Z. M. Ou, B. K. Spearman and K. S. Williams, “Elementary evaluation of certain convolution sums involving divisor function”, Number Theory for the Millennium II, eds. M. A. Bennett, B. C. Berndt, N. Boston, H. G. Diamond, A. J. Hildebrand, W. Philipp, A. K. Peters, 2002, 229-274.

To content of the issue