On trivial p-adic zeroes for elliptic curves over Kummer extensions

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.