  In this paper, we present some new nonexistence results on
$(m,n)$-generalized bent functions, which improved recent results. More
precisely, we derive new nonexistence results for general $n$ and $m$ odd or $m
\equiv 2 \pmod{4}$, and further explicitly prove nonexistence of
$(m,3)$-generalized bent functions for all integers $m$ odd or $m \equiv 2
\pmod{4}$. The main tools we utilized are certain exponents of minimal
vanishing sums from applying characters to group ring equations that
characterize $(m,n)$-generalized bent functions.
