p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas
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AbstractConsider an elliptic curve defined over an imaginary quadratic field K with good reduction at the primes above p ≥ 5 and with complex multiplication by the full ring of integers of K. In this paper, we construct p-adic analogues of the Eisenstein-Kronecker series for such an 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.
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2014 ◽
Vol 915-916
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pp. 1336-1340
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1998 ◽
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pp. 447-459
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pp. 826-843
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pp. 13-24
2016 ◽
Vol 164
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pp. 67-98
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