Title: Several Classes of Permutation Trinomials over $\mathbb F_{5^n}$ From Niho Exponents,
Abstract: The construction of permutation trinomials over finite fields attracts
people's interest recently due to their simple form and some additional
properties. Motivated by some results on the construction of permutation
trinomials with Niho exponents, by constructing some new fractional polynomials
that permute the set of the $(q+1)$-th roots of unity in $\mathbb F_{q^2}$, we
present several classes of permutation trinomials with Niho exponents over
$\mathbb F_{q^2}$, where $q=5^k$.