On the exceptional zeros of $p$-non-ordinary $p$-adic $L$-functions and a conjecture of Perrin-Riou

Denis Benois, Kazim Buyukboduk

Our goal in this article is to prove a form of $p$-adic Birch and Swinnerton-Dyer formula for the second derivative of the $p$-adic $L$-function associated to a newform $f$ which i…