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# Tiffany Necklace Replica a relation formula between the determinant

We construct a generalization of Demjanenko's matrix for an arbitrary imaginary abelian field and prove a relation formula between the determinant of this matrix and the relative class number. In a special case, we prove that the determinant of this matrix coincides with Maillet's determinant. As an application, we give an upper bound for the relative class number of any imaginary subfield ofQ(ζ2m).
In this note, we present an explicit form for the exit probability of an integrated geometric Brownian motion from a given curved domain. Explicit bounds for the exit probability and one possible application

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