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<p>In this article, new identities between Jacobi theta functions and Ramanujan theta functions are established. The key idea is to utilize the eigenvalues of the discrete Fourier transform (DFT) that have multiplicity one. This interplay between Fourier analysis and special functions reveals deeper connections within the theory of theta functions.</p>

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Jacobi and Ramanujan theta function identities arising from the discrete Fourier transform

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Hemant Masal

摘要

In this article, new identities between Jacobi theta functions and Ramanujan theta functions are established. The key idea is to utilize the eigenvalues of the discrete Fourier transform (DFT) that have multiplicity one. This interplay between Fourier analysis and special functions reveals deeper connections within the theory of theta functions.