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Using the methods developed for the proof that the 2-universality criterion is unique, we partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Ohs 8-universality criterion as an application of our characterization results.
If $L/K$ is a finite Galois extension of local fields, we say that the valuation criterion $VC(L/K)$ holds if there is an integer $d$ such that every element $x in L$ with valuation $d$ generates a normal basis for $L/K$. Answering a question of Byot
Let f:X->X be a morphism of a variety over a number field K. We consider local conditions and a Bruaer-Manin condition, defined by Hsia and Silverman, for the orbit of a point P in X(K) to be disjoint from a subvariety V of X, i.e., the intersection
In multi-terminal communication systems, signals carrying messages meant for different destinations are often observed together at any given destination receiver. Han and Kobayashi (1981) proposed a receiving strategy which performs a joint unique de
It was discovered some years ago that there exist non-integer real numbers $q>1$ for which only one sequence $(c_i)$ of integers $c_i in [0,q)$ satisfies the equality $sum_{i=1}^infty c_iq^{-i}=1$. The set of such univoque numbers has a rich topologi
We prove that the Coleman-Mazur eigencurve is proper over the weight space for any prime p and tame level N.