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Let $S$ be a fixed symmetric, invertible, $n \times n$ matrix and denote $I$ the identity matrix. Consider a function $f$ on the space of positive definite matrices defined by$$ f(P) = \operatorname{tr}\left[ (I + (P^{1/4} S P^{1/4})^2)^{-1} \right]...

This is a followup to this question, but I'll try to include all the currently relevant information here.
Background summary: I'm investigating polyhedra in R3 which are in some sense "area-minimizing", in analogy with smooth surfaces of constant mean curvature. In particular, given a particular combinatorial "type" of polyhedron homeomorphic to a sphere...

Let$$K:=L\left(2,\left(\frac{-3}{\cdot}\right)\right)=\sum_{k=1}^\infty\frac{(\frac k3)}{k^2}=\sum_{j=0}^\infty\left(\frac1{(3j+1)^2}-\frac1{(3j+2)^2}\right),$$ where $(\frac k3)$ is the Legendre symbol.Recently, I found the following (conjectural) curious...

I recently posted a short (6 page) note on arXiv, and have more or less decided that I should not submit it to a journal. I could have tacked it onto the end of a previous paper, but I thought it would be somewhat incongruous -- it is an interesting...