Spin coherent states, binomial convolution and a generalization of the Möbius function.

Abstract

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.