2015
DOI: 10.1017/s0027763000027148
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p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas

Abstract: Consider an elliptic curve defined over an imaginary quadratic field K with good reduction at the primes above p ≥ 5 and has complex multiplication by the full ring of integers OK of K. In this paper, we construct p-adic analogues of the Eisenstein-Kronecker series for such elliptic curve as Coleman functions on the elliptic curve. We then prove p-adic analogues of the first and second Kronecker limit formulas by using the distribution relation of the Kronecker theta function. K coln−m (0, z, n) := E col m,n (… Show more

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