Francisco Neto, Antônio2017-09-182017-09-182012FRANCISCO 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. 2017.1751-8121http://www.repositorio.ufop.br/handle/123456789/8735By 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.en-USrestritoArtigo publicado em periodicohttp://iopscience.iop.org/article/10.1088/1751-8113/45/39/395308http://dx.doi.org/10.1088/1751-8113/45/39/395308