منابع مشابه
Powerfree Values of Binary Forms
Given a binary form f(x; y) 2 Z[x; y], we will be interested in nding the smallest k for which we can establish that there are in nitely many integers a and b such that f(a; b) is k free. Necessarily, we require the f has no xed kth prime power divisor. Until the nal section of this paper, we will also consider f to be irreducible. We set n = deg f . For k = 2, this problem has recently become ...
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Given a suitable arithmetic function h : N → R>0, and a binary form F ∈ Z[x1, x2], we investigate the average order of h as it ranges over the values taken by F . A general upper bound is obtained for this quantity, in which the dependence upon the coefficients of F is made completely explicit.
متن کاملOn the Gaps between Values of Binary Quadratic Forms
Among the values of a binary quadratic form, there are many twins of fixed distance. This is shown in quantitative form. For quadratic forms of discriminant −4 or 8 a corresponding result is obtained for triplets.
متن کاملOn Orbits of SL(2,Z)+ and Values of Binary Quadratic Forms on Positive Integral Pairs
We consider actions of SL(2, ZZ) and SL(2, ZZ)+ (semigroup of matrices with nonnegative integral entries) on the projective space IP and on IP × IP . Results are obtained on orbit-closures under these actions and they are applied to describe a class of binary quadratic forms Q such that the sets Q(ZZ2) or Q(ZZ2 +) are dense in IR. We prove also a result generalising a theorem of Troessaert and ...
متن کاملSingular Values of Trilinear Forms
Let T : H1 H2 H3 ! C be a trilinear form where H1, H2, H3 are separable Hilbertspaces. In the hypothesis that at least two of the three spaces are nite dimensional weshow that the norm square = kTk2 is a root of a certain algebraic equation, usually ofvery high degree, which we baptize the milleniar equation, because it is an analogue ofthe secular equation in the bilinear c...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2012
ISSN: 0010-2571
DOI: 10.4171/cmh/264