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On the de Rham and -adic realizations of the elliptic polylogarithm for CM elliptic curves
In this paper, we give an explicit description of the de Rham and -adic polylogarithms for elliptic curves using the Kronecker theta function. In particular, consider an elliptic curve defined over an imaginary quadratic field with complex multiplication by the full ring of integers of . Note that our condition implies that has class number one. Assume in addition that has good reduction above a prime unramified in . In this case, we prove that the specializations of the -adic elliptic...
Specialization of the -adic polylogarithm to -th power roots of unity.
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