  The Aharonov-Bohm effect is traditionally attributed to the effect of the
electromagnetic 4-potential $A$, even in regions where both the electric field
$\mathbf{E}$ and the magnetic field $\mathbf{B}$ are zero. The AB effect
reveals that multiple-valued functions play a crucial role in the description
of an electromagnetic field. We argue that the quantity measured by AB
experiments is a difference in values of a multiple-valued complex function,
which we call a complex potential or {pre-potential. We show that any
electromagnetic field can be described by this pre-potential, and give an
explicit expression for the electromagnetic field tensor through this
potential. The pre-potential is a modification of the two scalar potential
functions.
