LAUSR

Abstract In this paper, we study the properties of Diophantine exponents w n and w n ⁎ for Laurent series over a finite field. We prove that for an integer n ≥ 1 and a rational number w > 2 n − 1 , there exist a strictly increasing sequence of positive integers ( k j ) j ≥ 1 and a sequence of algebraic Laurent series ( ξ j ) j ≥ 1 such that deg ⁡ ξ j = p k j + 1 and w 1 ( ξ j ) = w 1 ⁎ ( ξ j ) = … = w n ( ξ j ) = w n ⁎ ( ξ j ) = w for any j ≥ 1 . For each n ≥ 2 , we give explicit examples of Laurent series ξ for which w n ( ξ ) and w n ⁎ ( ξ ) are different.