▶Speaker : Mingyu Kim (Sungkyunkwan University)

▶Title : Tight universal quadratic forms

▶Abstract : For a positive integer $n$, let $T(n)$ be the set of all integers greater than or equal to $n$. An integral quadratic form $f$ is called tight $T(n)$-universal if the set of nonzero integers that are represented by $f$ is exactly $T(n)$. The smallest possible rank over all tight $T(n)$-universal quadratic forms is defined by $t(n)$. In this talk, we find all tight $T(n)$-universal diagonal quadratic forms. We also prove that $t(n) \in \Omega(\log_2(n)) \cap O(\sqrt{n})$. Explicit lower and upper bounds for $t(n)$ will be provided for some small integer $n$. This is a joint work with Byeong-Kweon Oh.

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