Spin coherent states, binomial convolution and a generalization of the M?bius function

摘要

By making use of a G?del-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?bius function obtained in Spector (1990 Commun. Math. Phys. 127 239) by giving a quantum mechanical interpretation of a generalization of the M?bius function: the Fleck function. We also show that inversion convolution theorem for the Liouville function and some key relations giving the M?bius 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.