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Arithmetical Fourier transforms and Hilbert space: Restoration of the lost legacy

Abstract : In this survey-type paper we show that the seemingly unrelated two fields-Chebyshev-Markov expansion (CME) [On83] and Arithmetical Fourier Transform (AFT) [Che10]-are indeed different looks of one entity, by the plausible missing link-Romanoff-Wintner theory (RWT). RWT generalizes both approaches, CME and AFR, and was developed in [Wi44] and [Ro51a], [Ro51b] which were written independently. These two lost researches are very closely related and effective for producing new number-theoretic identities. Cf. [CKT09] for fragmental restoration of them.
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https://hal.archives-ouvertes.fr/hal-03208314
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Submitted on : Monday, April 26, 2021 - 2:36:32 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Tuesday, July 27, 2021 - 7:08:28 PM

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J.-W Feng, S Kanemitsu, T Kuzumaki. Arithmetical Fourier transforms and Hilbert space: Restoration of the lost legacy. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020, pp.56-68. ⟨10.46298/hrj.2021.7426⟩. ⟨hal-03208314⟩

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