SOME CUBIC MODULAR IDENTITIES OF RAMANUJAN

Authors
BORWEIN JM BORWEIN PB GARVAN FG
Citation
Jm. Borwein et al., SOME CUBIC MODULAR IDENTITIES OF RAMANUJAN, Transactions of the American Mathematical Society, 343(1), 1994, pp. 35-47
Citations number
14
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
343
Issue
1
Year of publication
1994
Pages
35 - 47
Database
ISI
SICI code
0002-9947(1994)343:1<35:SCMIOR>2.0.ZU;2-0
Abstract
There is a beautiful cubic analogue of Jacobi's fundamental theta func tion identity: theta3(4) = theta4(4) + theta2(4) It is [GRAPHICS] Here omega = exp(2pii/3). In this note we provide an elementary proof of t his identity and of a related identity due to Ramanujan. We also indic ate how to discover and prove such identities symbolically.