$p$-adic Eisenstein-Kronecker functions and the elliptic polylogarithm for CM elliptic curves

Details $p$-adic Eisenstein-Kronecker functions and the elliptic polylogarithm for CM elliptic curves $p$-adic Eisenstein-Kronecker functions and the elliptic polylogarithm for CM elliptic curves

2008-07-25

arxiv.org/abs/0807.4007v1

Mathematics

Number Theory

Scientific paper

In this paper, we construct $p$-adic analogues of the Kronecker double
series, which we call the Eisenstein-Kronecker series, as Coleman functions on
an elliptic curve with complex multiplication. We then show that the periods of
the specialization of the $p$-adic elliptic polylogarithm sheaf to arbitrary
non-zero points of the elliptic curve may be expressed using these functions.

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