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 SIGMA 20 (2024), 096, 4 pages       arXiv:2401.00586     
https://doi.org/10.3842/SIGMA.2024.096 
 
Scale Invariant Scattering and Bernoulli Numbers
Thomas L. Curtright
 Department of Physics, University of Miami, Coral Gables, FL 33124, USA
 
 
Received June 07, 2024, in final form October 14, 2024; Published online October 24, 2024
 Abstract 
Non-relativistic quantum mechanical scattering from an inverse square potential in two spatial dimensions leads to a novel representation of the Bernoulli numbers.
 Key words: scale invariance; Bernoulli numbers; Riemann hypothesis. 
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References 
- Abramowitz M., Stegun I., Handbook of mathematical functions, United States  Department of Commerce, National Bureau of Standards, 1970.
 
- Curtright T., Mean sinc sums and scale invariant scattering, J. Math.  Phys. 65 (2024), 012104, 4 pages, arXiv:2212.13884.
 
- Curtright T., Vignat C., Scale invariant scattering in 2D, Bulg. J.  Phys. 51 (2024), 104-108, arXiv:2303.14861.
 
- 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.
 
- Gosper R.W., Ismail M.E.H., Zhang R., On some strange summation formulas,  Illinois J. Math. 37 (1993), 240-277.
 
- Herscovici O., Mansour T., The Miki-type identity for the  Apostol-Bernoulli numbers, Ann. Math. Inform. 46  (2016), 97-114.
 
- Luschny P.H.N., An introduction to the Bernoulli function,  arXiv:2009.06743.
 
- 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, available at  http://luschny.de/math/zeta/The-Bernoulli-Manifesto.html.
 
- Miki H., A relation between Bernoulli numbers, J. Number Theory  10 (1978), 297-302.
 
- Riesz M., Sur l'hypothèse de Riemann, Acta Math. 40  (1916), 185-190.
 
- Weisstein E.W., Bernoulli number, available at  https://mathworld.wolfram.com/BernoulliNumber.html.
 
 
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