Discrete Fourier Transform and Theta Function Identities

  • R. A. Malekar


The classical identities of the Jacobi theta functions are obtained from the multiplicities of the eigenvalues ik and the corresponding eigenvectors of the DFT Φ(n) expressed in terms of the theta functions. An extended version of the classical Watson addition formula and Riemann’s identity on theta functions is derived. Watson addition formula and Riemann’s identity are obtained as a particular case. An extensions of some classical identities corresponding to the theta functions θa,b(x, τ) with a,b\(\frac {1}{3}\mathbb {Z}\) are also derived.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • R. A. Malekar
    • 1
  1. 1.Department of MathematicsNational Defence AcademyKhadakwasla, PuneIndia

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