A refined non-vanishing theorem is proved for the p-adic logarithm of rational points on GL2-type abelian varieties associated to Hilbert modular newforms and Heegner points.
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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.
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A refined non-vanishing of the $p$-adic logarithm of a rational point on an abelian variety
A refined non-vanishing theorem is proved for the p-adic logarithm of rational points on GL2-type abelian varieties associated to Hilbert modular newforms and Heegner points.
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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.