A numerical approach toward the p-adic Beilinson conjecture for elliptic curves over $${\mathbb {Q}}$$

New p-adic hypergeometric functions and syntomic regulators

“…B]). Then, thanks to the main result of his paper [7], it follows that reg syn (ξ a ) gives the p-adic L-value of X 4 (see [3,Thm. 5.2] for the precise statement).…”

“…However there are only a few of literatures due to the extremal difficulty of the statement. In a joint paper [3] with Chida, we give a concise statement of the p-adic Beilinson conjecture by restricting ourselves to the case of elliptic curves over Q.…”

“…where x ∼ Q × y means xy ̸ = 0 and x/y ∈ Q × . We also refer to [3,Conj. 3.3] for more precise statement.…”

“…See Section 5.2 for other cases. The author has no idea how to attack the question in general, while we have one example (the proof relies on Brunault's paper [7] and his appendix in [3]).…”