Green’s Functions and Euler’s Formula for $$\zeta (2n)$$
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Publication:5011569
DOI10.1007/978-3-030-68490-7_3zbMath1469.11279OpenAlexW3170162724MaRDI QIDQ5011569
Mark S. Ashbaugh, Klaus Kirsten, Lance L. Littlejohn, Hagop Tossounian, Friedrich Gesztesy, Lotfi Hermi
Publication date: 27 August 2021
Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-030-68490-7_3
Riemann zeta functionGreen's functionBernoulli numbersDirichlet LaplacianBernoulli polynomialstrace formulastrace class operators
Exact enumeration problems, generating functions (05A15) (zeta (s)) and (L(s, chi)) (11M06) Spectrum, resolvent (47A10) Eigenvalue problems for linear operators (47A75)
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Cites Work
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- A simple proof that \(\zeta (2) = \frac {\pi^{2}}{6}\)
- A proof that Euler missed: Evaluating \(\zeta\) (2) the easy way
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- Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators
- Modified equations and the Basel problem
- A \(q\)-analogue for Euler's evaluations of the Riemann zeta function
- A new method of evaluating the sums of \(\sum^{\infty}_{k=1}(-1)^{k+1}k^{-2p}\), \(p = 1,2,3,\dots\) and related series
- The Basel Problem as a Rearrangement of Series
- A Short Elementary Proof of Σ 1/k2= π2/6
- The Basel Problem as a Telescoping Series
- Another proof of Euler’s formula for $\zeta(2k)$
- Euler and Infinite Series
- A Short Proof of ζ(2) = π<sup>2</sup>/6
- How to Compute Σ1/n2 by Solving Triangles
- Revisiting the Riemann Zeta function at positive even integers
- An Elementary Proof of the Formula \Sum ∞ k = 1 1/k 2 = π 2 /6
- Trace formulas for Sturm-Liouville differential operators
- A Simple Computation of ζ (2<em>k</em>)
- An Elementary Proof of ∑ ∞ n = 1 1/n 2 = π 2 /6
- The Series Σ<sup>∞</sup><sub>k = 1</sub>k<sup>-s</sup>, s = 2,3,4,⋯, Once More
- Euler and the Zeta Function
- Elementary Evaluation of ζ(2n)
- A Simple Proof of 1 + 1 2 2 + 1 3 2 + ⋯ = π 2 6 and Related Identities
- Another Simple Proof of 1 + 1 2 2 + 1 3 2 + ⋅⋅⋅ = π 2 6
- Finding ζ(2p) from a Product of Sines
- An Elementary Proof of Euler's Formula for z(2m)
- Simple Proofs for and sin
- Another Proof of the Formula ∑1/k 2 = π 2 /6
- On ∑<sup>∞</sup><sub>n = 1</sub> (1/n<sup>2k</sup>)
- Still Another Elementary Proof That Σ 1/k<sup>2</sup>=π<sup>2</sup>/6
- A Simple Proof of the Formula ∑ ∞ k = 1 = π 2 /6
- Another Elementary Proof of Euler's Formula for ζ(2n)
- Elementary Evaluation of ζ(2k )
- A recurrence formula for 𝜁(2𝑛)
- A New Method of Evaluating ζ(2n)
- Operator Theory