### On the coefficients of the characteristic series of the U-operator, by Robert F. Coleman

This paper has appeared in Proc. Nat. Acad. Sci. USA 94 (1997), no. 21,
11129-11132 and so the dvi version has been removed. We give a conceptual proof
of the fact that the coefficients of the characteristic
series of the $ U$-operator acting on families of overconvegent
modular forms lie in the Iwasawa algebra. We also
prove Theorem B6.2 of "$p$-adic Banach spaces and Families of
modular forms" which asserts that
this characteristic series ``controls'' forms of higher level.

Robert F. Coleman <coleman@math.berkeley.edu>