On a question of GOSS

초록

In this paper we answer the question raised by D. Goss in [Applications of non-Archimedean integration to the $L$-series of $\tau$-sheaves, {\em J. Number Theory,} 110 (2005), no. 1, 83--113] by proving that the group of (locally) analytic endomorphisms on the 1-units of a locally compact field of characteristic $p$ is isomorphic to the $p$-adic integers. Furthermore we derive a similar result for the $p$-adic numbers.