Results 31 to 40 of about 117,201 (178)
Nonnegative polynomials and their Carath\'eodory number
, 2014 In 1888 Hilbert showed that every nonnegative homogeneous polynomial with real coefficients of degree $2d$ in $n$ variables is a sum of squares if and only if $d=1$ (quadratic forms), $n=2$ (binary forms) or $(n,d)=(3,2)$ (ternary quartics).
Naldi, Simone
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The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
, 2003 We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)x(2n ...
Bart De Moor, J. Dehaene, Jeroen Dehaene
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The arithmetic of arithmetic Coxeter groups
, 2018 In the 1990s, J.H. Conway published a combinatorial-geometric method for analyzing integer-valued binary quadratic forms (BQFs). Using a visualization he named the "topograph," Conway revisited the reduction of BQFs and the solution of quadratic ...
Milea, Suzana +2 more
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The Endomorphism Rings of Supersingular Elliptic Curves over $\mathbb{F}_p$ and the Binary Quadratic Forms [PDF]
, 2022 Guanju Xiao +3 more
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Arab Journal of Basic and Applied SciencesMersenne primes, renowned for their captivating form as [Formula: see text] have intrigued mathematicians for centuries. In this paper, we embark on a captivating quest to unveil the intricate nature of Mersenne primes, seamlessly integrating methods ...
Moustafa Ibrahim
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Binary quadratic forms and the factorization method of Gauss [PDF]
, 2021 Monica Celis, Paulo Almeida
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Binary quadratic forms of determinant −pq
Journal of Number Theory, 1972 AbstractThe following theorem is proved: If p and q are distinct primes of the form 4n + 1, and (p | q) = 1, then x2 − pqy2 represents −1 if (p | q)4 = (q | p)4 = −1; p if (q | p)4 = −(p | q)4 = 1; q if (p | q)4 = −(q | p)4 = 1. If (p | q)4 = (q | p)4 = 1, there are examples with any of the three being represented.
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The birational composition of arbitrary quadratic form with binary quadratic form
Journal of the Belarusian State University. Mathematics and Informatics, 2022 Let f(X) and g(Y) be nondegenerate quadratic forms of dimensions m and n respectively over a field K, charK ≠ 2. Herein, the problem of the birational composition of f(X) and g(Y) is considered, namely, the condition is established when the product f(X)g(Y) is birationally equivalent over K to a quadratic form h(Z) over K of dimension m + n?
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Composition of Binary Quadratic Forms over Number Fields
, 2019 In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class number one.
Zemková, Kristýna
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On the least integers represented by the genera of binary quadratic forms [PDF]
, 1971 A. Baker, Andrzej Schinzel
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