dorsal/arxiv
View SchemaAnalytic Continuation of Bernoulli Numbers, a New Formula for the Riemann Zeta Function, and the Phenonmenon of Scattering of Zeros
| Authors | S. C. Woon |
|---|---|
| Categories | |
| ArXiv ID | physics/9705021 |
| URL | https://arxiv.org/abs/physics/9705021 |
Abstract
The method analytic continuation of operators acting integer n-times to complex s-times (hep-th/9707206) is applied to an operator that generates Bernoulli numbers B_n (Math. Mag. 70(1), 51 (1997)). B_n and Bernoulli polynomials B_n(s) are analytic continued to B(s) and B_s(z). A new formula for the Riemann zeta function zeta(s) in terms of nested series of zeta(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenonmenon of `scatterings' of the zeros of B_s(z) is observed.
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"abstract": "The method analytic continuation of operators acting integer n-times to\ncomplex s-times (hep-th/9707206) is applied to an operator that generates\nBernoulli numbers B_n (Math. Mag. 70(1), 51 (1997)). B_n and Bernoulli\npolynomials B_n(s) are analytic continued to B(s) and B_s(z). A new formula for\nthe Riemann zeta function zeta(s) in terms of nested series of zeta(n) is\nderived. The new concept of dynamics of the zeros of analytic continued\npolynomials is introduced, and an interesting phenonmenon of `scatterings\u0027 of\nthe zeros of B_s(z) is observed.",
"arxiv_id": "physics/9705021",
"authors": [
"S. C. Woon"
],
"categories": [
"math-ph",
"math.MP",
"nlin.CD"
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"title": "Analytic Continuation of Bernoulli Numbers, a New Formula for the Riemann Zeta Function, and the Phenonmenon of Scattering of Zeros",
"url": "https://arxiv.org/abs/physics/9705021"
},
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