Discrete Fourier Transform and Theta Function Identities

R. A. Malekar ()
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R. A. Malekar: National Defence Academy, Department of Mathematics

Chapter Chapter 2 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 55-99 from Springer

Abstract: Abstract The classical identities of the Jacobi theta functions are obtained from the multiplicities of the eigenvalues i k 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 θ a,b(x, τ) with a,b ∈ 1 3 ℤ $$\frac {1}{3}\mathbb {Z}$$ are also derived.

Date: 2019
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DOI: 10.1007/978-3-030-15242-0_2

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