On an identity of theta functions obtained from weight enumerators of linear codes
Tomoaki Murayama · Proceedings of the Japan Academy Series A Mathematical Sciences · 1998
Maher obtained an identity of theta functions by means of the Lee weight enumerators of linear codes over finite fields.S. S. Rangachari used it to prove an identity of theta functions conjectured by S. Ramanujan.In this paper, we consider the linear codes over finite rings, and give a generalization of Maher's identity.As an application, we generalize the result of Rangachari.1. Introduction.Let a/n and b/n be rational numbers with lal, Ibl < n, We define the Jacobi theta function with a characteristic (a/n, b n) by