Delbourgo, Daniel2015-11-1620142015-11-162014Delbourgo, D. (2014). Exceptional zeros of p-adic L-functions over non-abelian extensions. Glasgow Mathematical Journal, First View. http://doi.org/10.1017/S00170895150002451469-509Xhttps://hdl.handle.net/10289/9749Suppose E is an elliptic curve over , and p > 3 is a split multiplicative prime for E. Let q = p be an auxiliary prime, and fix an integer m coprime to pq. We prove the generalised Mazur–Tate–Teitelbaum conjecture for E at the prime p, over number fields K ⊂ μq∞ , q∞√m such that p remains inert in K ∩ (μq∞ ) +. The proof makes use of an improved p-adic L-function, which can be associated to the Rankin convolution of two Hilbert modular forms of unequal parallel weight.application/pdfenThe is an accepted version of an article published in the journal: Glasgow Math. © 2015 Glasgow Mathematical Journal Trust.Journal Article10.1017/S0017089515000245