INDEX OF MAXIMALITY AND GOSS ZETA FUNCTION

摘要

In this article, we define the index of maximality m(y) of a positive integer y, associated with the vanishing of certain power sums over F-q[T], related to the set V-m(y) of "valid" decompositions of y = X-1 vertical bar ... vertical bar X-m of length m. The index of maximality determines the maximum positive integer m for which the sets V-m(y) are not empty. An algorithm is provided to find V-i(y), 1 <= i <= m(y) explicitly.