I have two matrices A and B that each are associated with their Dirichlet generating functions. One Dirichlet generating function per matrix that is.
Now it is very probable that the most negative eigenvalue of the symmetric matrix A.B or B.A is approximately a prime number.
Would it make sense to figure out the Dirichlet generating function for the commutator A.B-B.A?
Also, how is this related to the uncertainty principle? I mean I know with certainty what the Dirichlet generating functions for A and B are. But that is not what is meant by uncertainty in the uncertainty principle, is it?