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Proceedings of the Steklov Institute of Mathematics : Volume 296

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Proceedings of the Steklov Institute of Mathematics : Volume 294, Issue 1, Supplement,October 2016

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On upper bounds in the Fröhlich polaron model

Exact solutions of the Euler equations for some two-dimensional incompressible flows

Estimates for the widths of discrete function classes generated by a two-weight summation operator

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Elliptic function of level 4

Content Provider	Springer Nature Link
Author	Bunkova, E. Yu.
Copyright Year	2016
Abstract	The article is devoted to the theory of elliptic functions of level n. An elliptic function of level n determines a Hirzebruch genus called an elliptic genus of level n. Elliptic functions of level n are also of interest because they are solutions of the Hirzebruch functional equations. The elliptic function of level 2 is the Jacobi elliptic sine function, which determines the famous Ochanine–Witten genus. It is the exponential of the universal formal group of the form F(u, v) = (u $^{2}$ − v $^{2}$)/(uB(v) − vB(u)), B(0) = 1. The elliptic function of level 3 is the exponential of the universal formal group of the form F(u, v) = (u $^{2}$ A(v) − v $^{2}$ A(u))/(uA(v)$^{2}$ − vA(u)$^{2}$), A(0) = 1, A″(0) = 0. In the present study we show that the elliptic function of level 4 is the exponential of the universal formal group of the form F(u, v) = (u $^{2}$ A(v) − v $^{2}$ A(u))/(uB(v) − vB(u)), where A(0) = B(0) = 1 and for B′(0) = A″(0) = 0, A′(0) = A $_{1}$, and B″(0) = 2B $_{2}$ the following relation holds: (2B(u) + 3A $_{1}$ u)$^{2}$ = 4A(u)$^{3}$ − (3A $_{1}$ $^{2}$ − 8B $_{2}$)u $^{2}$ A(u)$^{2}$. To prove this result, we express the elliptic function of level 4 in terms of the Weierstrass elliptic functions.
Starting Page	201
Ending Page	214
Page Count	14
File Format	PDF
ISSN	00815438
Journal	Proceedings of the Steklov Institute of Mathematics
Volume Number	294
Issue Number	1
e-ISSN	15318605
Language	English
Publisher	Pleiades Publishing
Publisher Date	2016-10-23
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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