Divisors of the Euler and Carmichael functions

We study the distribution of divisors of Euler's totient function and Carmichael's function. In particular, we estimate how often the values of these functions have "dense" divisors.Comment: v.3, 11 pages. To appear in Acta Arithmetica. Very small corrections and changes suggested by the referee. Added abstract, keywords, MS

Simultaneous bistability of qubit and resonator in circuit quantum electrodynamics

We explore the joint activated dynamics exhibited by two quantum degrees of freedom: a cavity mode oscillator which is strongly coupled to a superconducting qubit in the strongly coherently driven dispersive regime. Dynamical simulations and complementary measurements show a range of parameters where both the cavity and the qubit exhibit sudden simultaneous switching between two metastable states. This manifests in ensemble averaged amplitudes of both the cavity and qubit exhibiting a partial coherent cancellation. Transmission measurements of driven microwave cavities coupled to transmon qubits show detailed features which agree with the theory in the regime of simultaneous switching

Quaternionic Artin representations of Q

Isomorphism classes of dihedral Artin representations of ℚ can be counted asymptotically using Siegel's asymptotic averages of class numbers of binary quadratic forms. Here we consider the analogous problem for quaternionic representations. While an asymptotic formula is out of our reach in this case, we show that the asymptotic behaviour in the two cases is quite different