分野別セミナー

講演概要：The minimal absolute value $\sigma_{\ell}(n)$ of a weight-$n$ sum of $\ell$-th roots of unity, for all $n$ and a fixed $\ell$, is an interesting value in the study of maximal determinant matrices. In the cases where $\ell=2,3,4, or 6$, this minimal absolute value is either $0$ or $1$. Thus $\ell=5$ constitutes the smallest non-trivial case. In this talk I will discuss recent results in collaboration with Akihiro Munemasa, where we determined $\sigma_5(n)$ for all $n\geq 1$. This problem turns out to be related to the Diophantine approximation of the golden ratio, and can be tackled using the theory of continued fractions.