  One-dimensional Yang-Mills-Nahm models are considered from algebrogeometric
points of view. A quasiclassical quantization of the models based on path
integral and its zeta function representation in terms of a Green function
diagonal for a heat equation with an elliptic potential is considered. The
Green function diagonal and, hence, zeta function and its derivative are
expressed via solutions of Hermit equation and, alternatively, by means of
Its-Matveev formalism in terms of Riemann teta-functions.
  For the Nahm model, which field is represented via elliptic (lemniscate)
integral by construction, one-loop quantum corrections to action are evaluated
as the zeta function derivative in zero point in terms of a hyperelliptic
integral. The alternative expression should help to link the representations
and continue investigation of the Yang-Mills-Nahm models.
  Keywords: Nahm model, one-loop quantum corrections, zeta function, elliptic
potential, hyperelliptic integral, Its-Matveev formula. MSC numbers: 81Q30,
35J10, 35K08, 81T13.
