The root lattice A*(n) and Ramanujan's circular summation of theta functions

Authors
Chua, KS
Citation
Ks. Chua, The root lattice A*(n) and Ramanujan's circular summation of theta functions, P AM MATH S, 130(1), 2001, pp. 1-8
Citations number
10
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
130
Issue
1
Year of publication
2001
Pages
1 - 8
Database
ISI
SICI code
0002-9939(2001)130:1<1:TRLAAR>2.0.ZU;2-O
Abstract
We relate a formula of Ramanujan on the circular summation of the nth power of theta functions, F-n(q), to the theta series of the root lattice A*(n). We then use properties of the lattice to show that F-n includes an SL2(Z) modular form when n is an odd perfect square as well as to derive a very si mple expression for F-9(q).