Spin coherent states, binomial convolution and a generalization of the Möbius function.
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2012
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By making use of a G¨odel-type relabeling of quantum states we show that
spin coherent states play a fundamental role in number theory. We generalize
the representation of the M¨obius function obtained in Spector (1990 Commun.
Math. Phys. 127 239) by giving a quantum mechanical interpretation of a
generalization of the M¨obius function: the Fleck function. We also show that
inversion convolution theorem for the Liouville function and some key relations
giving theM¨obius inversion theorem can be understood from the orthogonality
properties of the spin coherent states. Our results show a fruitful interplay of
quantum mechanics and number theory.
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FRANCISCO NETO, A. Spin coherent states, binomial convolution and a generalization of the Möbius function. Journal of Physics. A, Mathematical and Theoretical, v. 45, p. 395308, 2012. Disponível em: <http://iopscience.iop.org/article/10.1088/1751-8113/45/39/395308>. Acesso em: 20 jul. 2017.