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Parseval's Identity and Values of Zeta Function at Even Integers

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arxiv 1709.09326 v1 pith:R4BHLEOG submitted 2017-09-27 math.NT

Asghar Ghorbanpour , Michelle Hatzel This is my paper · ORCID
classification math.NT
keywords functionvaluesevenidentityintegersparsevalzetaapply
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Historically known as the Basel problem, evaluating the Riemann zeta function at two has resulted in numerous proofs, many of which have been generalized to compute the function's values at even positive integers. We apply Parseval's identity to the Bernoulli polynomials to find such values.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hierarchical separation of relaxation timescales from spectral localization bounds

    quant-ph 2026-06 unverdicted novelty 6.0 of 10

    Strong system-bath coupling induces a bright-dark structure in the effective coupling operator, producing a hierarchy of population relaxation timescales via spectral localization bounds on the Liouvillian in the reac...

  2. Basel problem: a physicist's solution

    math.HO 2019-08 accept novelty 5.0 of 10

    A physicist-style proof using Coulomb forces and the digamma function derives zeta(2) equals pi squared over 6, and by extension all even zeta values.

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