Leopoldt's conjecture.

### What is the conjecture
This says that if we have a basis $$e_i$$ of the unit group of a number field and $$p$$ is a prime number, then the matrix whose entries are $$\log_p(\sigma_j(e_i))$$ has non-zero determinant. Where $$\sigma_j$$ are the p-adic complex embeddings of K and $$\log_p$$ is the p-adic log.

See: https://encyclopediaofmath.org/wiki/Leopoldt_conjecture

### Prerequisites needed
p-adic complex embeddings and maybe p-adic logs.