Bull. Korean Math. Soc. 2012; 49(1): 155-163
Printed January 1, 2012
https://doi.org/10.4134/BKMS.2012.49.1.155
Copyright © The Korean Mathematical Society.
Dohyeong Kim
Pohang University of Science and Technology
Let $E$ be an elliptic curve over $\mathbb Q$. Using Iwasawa theory, we give what seems to be the first general upper bound for the order of vanishing of the $p$-adic $L$-function at $s=0$, and the $\mathbb Z_p$-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes $p$.
Keywords: good ordinary reduction, Tate-Shafarevich group, elliptic curves, Iwasawa theory
MSC numbers: 11G05
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