The paper under review constructs the p-adic L-function associated to the symmetric square of the Tate-module of an elliptic curve E. The curve E must be modular, and has to have good ordinary reduction at p. The construction follows the usual lines: We start with the complex L- function, which is analytic by Rankin’s method \((+\) careful checking at primes of bad reduction), and then one interpolates its special values. It is conjectured that these p-adic L-series are related to certain Iwasawa-modules (essentially a flat \(H^ 1\) at the second symmetric square): In the case of CM-curves theses conjectures are derived from more established ones (”two variable main conjecture”), and some assertions can be shown unconditionally.
There are many technical difficulties, which make things somehow less simple than in this description.