Abstract. Let Z/n denote the integers mod n and let % denote the finite Fourier transform on L\Z/n). We let ©2$), » F operate on ©2L2(Z/n) and show that ©2L2(Z/n) can be given a graded algebra structure (with no zero divisors) such that f(/g) ■ " ^U)^(g). We do this by establishing a natural isomorphism with the algebra of theta functions with period i. In addition, we find all algebra structures on 02L2(Z/n) satisfying the above condition. Introduction. Let Z/n denote the integers modulo n and form L = 0 2 L2(Z/ri). Let W „ denote the Fourier transform on L2(Z/ri) and let £F denote the linear transformation of L such tha
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