  We consider a class of models of non-equilibrium electronic Mach-Zehnder
interferometers built on integer quantum Hall edges states. The models are
characterized by the electron-electron interaction being restricted to the
inner part of the interferometer and transmission coefficients of the quantum
quantum point contacts, defining the interferometer, which may take arbitrary
values from zero to one. We establish an exact solution of these models in
terms of single-particle quantities --- determinants and resolvents of Fredholm
integral operators. In the general situation, the results can be obtained
numerically. In the case of strong charging interaction, the operators acquire
the block Toeplitz form. Analyzing the corresponding Riemann-Hilbert problem,
we reduce the result to certain singular single-channel determinants (which are
a generalization of Toeplitz determinants with Fisher-Hartwig singularities),
and obtain an analytic result for the interference current (and, in particular,
for the visibility of Aharonov-Bohm oscillations). Our results, which are in
good agreement with experimental observations, show an intimate connection
between the observed "lobe" structure in the visibility of Aharonov-Bohm
oscillations and multiple branches in the asymptotics of singular integral
determinants.
