A new construction of \({\mathfrak p}\)-adic L-functions attached to certain elliptic curves with complex multiplication
Although there now exists a vast literature on the p-adic L-functions attached to primes of ordinary reduction of an elliptic curve E, few works have been concerned with the case of supersingular primes. In this paper, the author restricts to the case of complex multiplications, and constructs a one-variable p-adic L-function in both cases, under a standard assumption on the field generated by the torsion points of E. The construction is based on interpolation of Eisenstein series. It would be interesting to compare the p-adic period occuring in this method with those given by Hodge-Tate theory. The article is complemented by a p-adic analogue of the Kronecker limit formula, and by a study of the L- functions having a pole at \(s=0\).
scientific article; zbMATH DE number 3983358
scientific article