On the explicit solutions of the elliptic Calogero system
Abstract
Let
q
1
,
q
2
,...,
q
N
be the coordinates of
N
particles on the circle, interacting with the integrable potential
∑
N
j<k
℘(
q
j
−
q
k
)
, where
℘
is the Weierstrass elliptic function. We show that every symmetric elliptic function in
q
1
,
q
2
,...,
q
N
is a meromorphic function in time. We give explicit formulae for these functions in terms of genus
N−1
theta functions.