ON IHARAS POWER-SERIES

We give a new simple proof to Ihara's conjecture on the coefficients of his power series interpolating Jacobi sums as an application of the method of proof of our congruence for the Gauss sums previously obtained by the author. More precisely, we will determine the coefficients (mod l(n)) of the Gauss sum power series, which is defined naturally in terms of Gauss sum. As an application, we get Anderson's power series and Ihara's power series. (C) 1995 Academic Press, Inc.