RAMANUJANS REMARKABLE PRODUCT OF THETA-FUNCTIONS

Authors
BERNDT BC CHAN HH ZHANG LC
Citation
Bc. Berndt et al., RAMANUJANS REMARKABLE PRODUCT OF THETA-FUNCTIONS, Proceedings of the Edinburgh Mathematical Society, 40, 1997, pp. 583-612
Citations number
16
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the Edinburgh Mathematical Society → ACNP
ISSN journal
00130915
Volume
40
Year of publication
1997
Part
3
Pages
583 - 612
Database
ISI
SICI code
0013-0915(1997)40:<583:RRPOT>2.0.ZU;2-8
Abstract
On pages 338 and 339 in his first notebook, Ramanujan records eighteen values for a certain product of theta-functions depending on two inte gral parameters m and n. When (m, n) = 1, it can be seen that each of these values is a unit. The purpose of this paper is to establish each of these eighteen values and to prove that under certain general cond itions this product is indeed a unit. Lastly, we prove that certain qu otients of theta-functions are algebraic integers.