On trivial p-adic zeroes for elliptic curves over Kummer extensions
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This article has been published in New Zealand Journal of Mathematics. Used with permission.
Abstract
We prove the exceptional zero conjecture is true for semistable elliptic curves E/Q over number fields of the form F(e²ⁿⁱ⁄ｑⁿ, ∆₁¹⁄ｑⁿ , . . . , ∆₁¹⁄ⁿd) where F is a totally real field, and the split multiplicative prime p ≠ 2 is inert in F(e²ⁿⁱ⁄ｑⁿ) ∩ R.
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Delbourgo, D. (2015). On trivial p-adic zeroes for elliptic curves over Kummer extensions. New Zealand Journal of Mathematics, 45, 33–38.
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NZ Mathematical Society