The root lattice and Ramanujan's circular summation of theta functions

Author:
Kok Seng Chua

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1-8

MSC (2000):
Primary 11B65, 11E20

DOI:
https://doi.org/10.1090/S0002-9939-01-06080-4

Published electronically:
May 3, 2001

MathSciNet review:
1855612

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We relate a formula of Ramanujan on the circular summation of the th power of theta functions, , to the theta series of the root lattice . We then use properties of the lattice to show that includes an modular form when is an odd perfect square as well as to derive a very simple expression for .

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Additional Information

**Kok Seng Chua**

Affiliation:
Institute of High Performance Computing, 89C Science Park Driver, #02-11/12 The Rutherford, Singapore 118261

Email:
chuaks@ihpc.nus.edu.sg

DOI:
https://doi.org/10.1090/S0002-9939-01-06080-4

Keywords:
Ramanujan,
theta functions,
lattices

Received by editor(s):
May 12, 2000

Published electronically:
May 3, 2001

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2001
American Mathematical Society