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Discrete Fourier Transform φ(3) and θa,b(x, T) for a,b ∈ 1/3Z
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The identities of theta functions θa,b(x, T) for a,b ∈ 1/3Z derived using properties of eigenvectors corresponding to the discrete Fourier transform φ(3). These identities are natural extensions of classical identities of Jacobi theta functions. In particular a quadratic identity and fourth order identity is obtained corresponding to theta functions on 1/3Z.
Keywords
Discrete Fourier Transform, Theta Functions on 1/3Z, Quadratic Identity for Theta Functions on 1/3Z.
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