Yasufumi Hashimoto

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It is well known that the problem to solve a set of randomly chosen multivariate quadratic equations over a finite field is NP-hard. However, when the number of variables is much larger than the number of equations, it is not necessarily difficult to solve equations. In fact, when n ≥ m(m+1) (n, m are the numbers of variables and equations respectively) and(More)
The aim of the present paper is to study the distributions of the length multi-plicities for negatively curved locally symmetric Riemannian manifolds. In Theorem 2.1, we give upper bounds of the length multiplicities and the square sums of them for general (not necessarily compact) cases. Furthermore in Theorem 2.3, we obtain more precise estimates of the(More)