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>