Establishes a relationship between non-vanishing of the E[p]-component in the class group of the p-division field and p-divisibility of the leading coefficient of the p-adic L-function when analytic rank is 1.
Schneider.p-adic height pairings
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On $p$-adic $L$-functions of elliptic curves and the ideal class groups of the division fields
Establishes a relationship between non-vanishing of the E[p]-component in the class group of the p-division field and p-divisibility of the leading coefficient of the p-adic L-function when analytic rank is 1.