Similarity of Quadratic Forms Over Global Fields in Characteristic 2
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DOI: 10.1007/s00006-019-1006-8
Abstract: Let K be a global function field of characteristic 2. For each non-trivial place v of K, let $$ K_{v} $$ be the completion of K at v. We show that if two non-degenerate quadratic… read more here.
Keywords: global fields; fields characteristic; quadratic forms; forms global ... See more keywords
Copositive and Positive Quadratic Forms on Matrices
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DOI: 10.1007/s00025-019-1079-7
Abstract: A real symmetric quadratic form \(f = f(Z_1,\ldots ,Z_n)\) in the n non-commuting indeterminates \(Z_1,\ldots ,Z_n\) is said to be d-positive (respectively, d-copositive) if for all real symmetric (respectively, positive semidefinite) \((d \times d)\)-matrices \(A_1,\ldots… read more here.
Keywords: quadratic forms; copositive positive; positive quadratic; forms matrices ... See more keywords
Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables
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DOI: 10.1007/s00208-016-1448-4
Abstract: Let $$-d$$-d be a a negative discriminant and let T vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $$-d$$-d. We prove an asymptotic formula for… read more here.
Keywords: averages fourier; siegel modular; coefficients siegel; binary quadratic ... See more keywords
Around 16-dimensional quadratic forms in $$I^3_q$$Iq3
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DOI: 10.1007/s00209-016-1714-x
Abstract: We determine the indexes of all orthogonal Grassmannians of a generic 16-dimensional quadratic form in $$I^3_q$$Iq3. This is applied to show that the 3-Pfister number of the form is $$\ge $$≥4. Other consequences are: a… read more here.
Keywords: quadratic forms; around dimensional; dimensional quadratic; forms iq3 ... See more keywords
Classification of 3-dimensional pairs of quadratic forms over a field
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DOI: 10.1016/j.jalgebra.2019.10.043
Abstract: Abstract By an n-dimensional quadratic form over a field F (F-form) we mean a homogeneous quadratic polynomial in n variables with coefficients in F. We call two pairs of n-dimensional quadratic F-forms ( f 1… read more here.
Keywords: classification; field; quadratic forms; classification dimensional ... See more keywords
Intersections of binary quadratic forms in primes and the paucity phenomenon
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DOI: 10.1016/j.jnt.2021.06.035
Abstract: Abstract. The number of solutions to a+b = c+d ≤ x in integers is a well-known result, while if one restricts all the variables to primes Erdős [4] showed that only the diagonal solutions, namely,… read more here.
Keywords: binary quadratic; primes paucity; paucity; quadratic forms ... See more keywords
Integral quadratic forms and graphs
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DOI: 10.1016/j.laa.2019.09.032
Abstract: Abstract The structure of an undirected graph is completely determined by a symmetric matrix: its adjacency matrix with respect to an ordering of its vertices; and that matrix can be used to define an integral… read more here.
Keywords: integral quadratic; forms graphs; quadratic forms;
PRIME-UNIVERSAL QUADRATIC FORMS $ax^{2}+by^{2}+cz^{2}$ AND $ax^{2}+by^{2}+cz^{2}+dw^{2}$
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DOI: 10.1017/s0004972719001023
Abstract: A positive-definite diagonal quadratic form $a_{1}x_{1}^{2}+\cdots +a_{n}x_{n}^{2}\;(a_{1},\ldots ,a_{n}\in \mathbb{N})$ is said to be prime-universal if it is not universal and for every prime $p$ there are integers $x_{1},\ldots ,x_{n}$ such that $a_{1}x_{1}^{2}+\cdots +a_{n}x_{n}^{2}=p$ . We… read more here.
Keywords: universal quadratic; quadratic forms; forms prime; prime universal ... See more keywords
APPLICATIONS OF SYSTEMS OF QUADRATIC FORMS TO GENERALISED QUADRATIC FORMS
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DOI: 10.1017/s0004972720000106
Abstract: ‎A system of quadratic forms is associated to every generalized quadratic form over a division algebra with involution of the first kind in characteristic two‎. ‎It is shown that this system determines the isotropy behaviour… read more here.
Keywords: systems quadratic; quadratic forms; generalised quadratic; generalized quadratic ... See more keywords
On quadratic forms in multivariate generalized hyperbolic random vectors
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DOI: 10.1093/biomet/asaa067
Abstract: Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression… read more here.
Keywords: multivariate generalized; quadratic forms; random vectors; generalized hyperbolic ... See more keywords
Static Linear Anti-Windup Design With Sign-Indefinite Quadratic Forms
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DOI: 10.1109/lcsys.2022.3182286
Abstract: We design static anti-windup gains to mitigate the effect of input saturation in linear output feedback closed loops. The design is conducted with the help of a non-quadratic Lyapunov function involving sign-indefinite quadratic forms, which… read more here.
Keywords: anti windup; sign indefinite; quadratic forms; design ... See more keywords