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A new construction of $${\mathfrak p}$$-adic L-functions attached to certain elliptic curves with complex multiplication. (English) Zbl 0608.14015
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 $$s=0$$.
Reviewer: D.Bertrand

##### MSC:
 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 14K22 Complex multiplication and abelian varieties 14H45 Special algebraic curves and curves of low genus 11S40 Zeta functions and $$L$$-functions 14G20 Local ground fields in algebraic geometry 14H20 Singularities of curves, local rings 14H52 Elliptic curves
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