Diophantine equations defined by binary quadratic forms over rational function fields
, 2019 We study the ``imaginary" binary quadratic form equations ax^2+bxy+cy^2+g=0 over k[t] in rational function fields, showing that a condition with respect to the Artin reciprocity map, is the only obstruction to the local-global principle for integral ...
Lv, Chang
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The automorphism group of an affine quadric
, 2006 We determine the automorphism group for a large class of affine quadric hypersurfaces over a field, viewed as affine algebraic varieties. In particular, we find that the group of real polynomial automorphisms of the n-sphere is just the orthogonal group ...
BURT TOTARO, Karpenko, Knebusch, Lam
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Equivalent Binary Quadratic Form and the Extended Modular Group [PDF]
, 2012 Extended modular group $\bar{\Pi}=$, where $ R:z\rightarrow -\bar{z}, \sim T:z\rightarrow\frac{-1}{z},\simU:z\rightarrow\frac{-1}{z +1} $, has been used to study some properties of the binary quadratic forms whose base points lie in the point set ...
malik, M. Aslam, Riaz, Muhammad
core
A proof of the S-genus identities for ternary quadratic forms [PDF]
, 2011 In this paper we prove the main conjectures of Berkovich and Jagy about weighted averages of representation numbers over an S-genus of ternary lattices (defined below) for any odd squarefree S \in N.
Berkovich, Alexander +2 more
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An elementary proof of Hilbert's theorem on ternary quartics [PDF]
, 2010 In 1888, Hilbert proved that every non-negative quartic form f=f(x,y,z) with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and used advanced methods from topology and algebraic geometry.
Pfister, Albrecht, Scheiderer, Claus
core
Parametrizing quartic algebras over an arbitrary base [PDF]
, 2010 We parametrize quartic commutative algebras over any base ring or scheme (equivalently finite, flat degree four $S$-schemes), with their cubic resolvents, by pairs of ternary quadratic forms over the base.
Wood, Melanie Matchett
core
Brill-Gordan Loci, Transvectants and an Analogue of the Foulkes Conjecture
, 2004 Combining a selection of tools from modern algebraic geometry, representation theory, the classical invariant theory of binary forms, together with explicit calculations with hypergeometric series and Feynman diagrams, we obtain the following ...
Abdesselam, Abdelmalek +1 more
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Discovery of an Ideal Quadratic Nodal Point in Two-Dimensional Binary Compound C<sub>5</sub>P<sub>1</sub>. [PDF]
ACS OmegaLi Y.
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Quantum annealing for inverse kinematics in robotics. [PDF]
Sci RepSalloum H +5 more
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Response Surface Optimization of High-Durability Fly Ash-Slag Blended Concrete as an Eco-Friendly Repair Material. [PDF]
Materials (Basel)Wei H, Chen A, Li C, Zhang J, Lu H.
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