The Journal of the Indian Mathematical Society

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Discrete Fourier Transform φ(3) and θa,b(x, T) for a,b ∈ 1/3Z


Affiliations
1 National Defence Academy, Pune-411 023, India
     

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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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  • Discrete Fourier Transform φ(3) and θa,b(x, T) for a,b ∈ 1/3Z

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Authors

R. A. Malekar
National Defence Academy, Pune-411 023, India

Abstract


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.

References