On the automorphic functions on $SL(m, \mathbb R)$.

This paper contains the method of expansion for the functions $F\colon SL(m, \mathbb R)\to\mathbb C^h$ which are automorphic with respect to the congruence subgroup in $SL(m, \mathbb Z)$. A preliminary form of expansion is provided by theorem 1 and a final one-by theorem 4. The ordinary Fourie expansion – $m=2$ – is a particular case of our one. Theorems 2, 3 provides the comparison of this expansion with another one [5].