2 problems

Representation-number doubling conjecture. Under these hypotheses, such a matrix $T'$ exists and the representation number satisfies the displayed doubling identity. The claim conc…

Let $F$ be a totally real number field of class number one in which $2$ is inert, and let $A_F$ be its ring of integers. Suppose that $2S(A_F^\times)^2$ is the squarefree determina…