Scale Invariant Scattering and Bernoulli Numbers
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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Non-relativistic quantum mechanical scattering from an inverse square potential in two spatial dimensions leads to a novel representation of the Bernoulli numbers.
Keywords: Bernoulli numbers, Riemann hypothesis.
Mots-clés : scale invariance
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Thomas L. Curtright. Scale Invariant Scattering and Bernoulli Numbers. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a95/

[1] Abramowitz M., Stegun I., Handbook of mathematical functions, United States Department of Commerce, National Bureau of Standards, 1970

[2] Curtright T., “Mean sinc sums and scale invariant scattering”, J. Math. Phys., 65 (2024), 012104, 4 pp., arXiv: 2212.13884 | DOI

[3] Curtright T., Vignat C., “Scale invariant scattering in 2D”, Bulg. J. Phys., 51 (2024), 104–108, arXiv: 2303.14861 | DOI

[4] Dunne G.V., Schubert C., “Bernoulli number identities from quantum field theory and topological string theory”, Commun. Number Theory Phys., 7 (2013), 225–249, arXiv: math.NT/0406610 | DOI

[5] Gosper R.W., Ismail M.E.H., Zhang R., “On some strange summation formulas”, Illinois J. Math., 37 (1993), 240–277 | DOI

[6] Herscovici O., Mansour T., “The Miki-type identity for the Apostol–Bernoulli numbers”, Ann. Math. Inform., 46 (2016), 97–114

[7] Luschny P.H.N., An introduction to the Bernoulli function, arXiv: 2009.06743

[8] Luschny P.H.N., The Bernoulli manifesto. A survey on the occasion of the 300-th anniversary of the publication of Jacob Bernoulli's Ars Conjectandi, 1713–2013 http://luschny.de/math/zeta/The-Bernoulli-Manifesto.html

[9] Miki H., “A relation between Bernoulli numbers”, J. Number Theory, 10 (1978), 297–302 | DOI

[10] Riesz M., “Sur l'hypothèse de Riemann”, Acta Math., 40 (1916), 185–190 | DOI

[11] Weisstein E.W., Bernoulli number, https://mathworld.wolfram.com/BernoulliNumber.html