Results 1 to 10 of about 220,587 (227)
Heights and Quadratic Forms: Cassels’ Theorem and its Generalizations [PDF]
, 2012 In this survey paper, we discuss the classical Cassels' theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings, as well as to more general situations, such as existence of totally ...
L. Fukshansky
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Most totally real fields do not have universal forms or the Northcott property. [PDF]
Proc Natl Acad Sci U S ASignificance The classical fact that every positive integer is a sum of four squares led to the much more general study of universal quadratic forms.
Daans N +4 more
europepmc +2 more sources
On Kitaoka's conjecture and lifting problem for universal quadratic forms [PDF]
Bulletin of the London Mathematical Society, 2021 For a totally positive definite quadratic form over the ring of integers of a totally real number field K$K$ , we show that there are only finitely many totally real field extensions of K$K$ of a fixed degree over which the form is universal (namely ...
Vítězslav Kala, Pavlo Yatsyna
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Wide moments of L-functions I : Twists by class group characters of imaginary quadratic fields [PDF]
Algebra & Number Theory, 2021 We calculate certain "wide moments" of central values of Rankin--Selberg $L$-functions $L(\pi\otimes \Omega, 1/2)$ where $\pi$ is a cuspidal automorphic representation of $\mathrm{GL}_2$ over $\mathbb{Q}$ and $\Omega$ is a Hecke character (of conductor ...
A. Nordentoft
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IEEE Transactions on Information Theory, 2023 The generalized Hamming weight of linear codes is a natural generalization of the minimum Hamming distance. They convey the structural information of a linear code and determine its performance in various applications, and have become one of important research topics in coding theory. Recently, Li (IEEE Trans. Inf.
Chao Liu, Dabin Zheng, Xiaoqiang Wang
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The Artin-Springer Theorem for quadratic forms over semi-local rings with finite residue fields [PDF]
, 2016 Let $R$ be a commutative and unital semi-local ring in which 2 is invertible. In this note, we show that anisotropic quadratic spaces over $R$ remain anisotropic after base change to any odd-degree finite \'{e}tale extension of $R$.
Stephen Scully
semanticscholar +1 more source
Forms over fields and Witt's lemma [PDF]
Mathematica Scandinavica, 2018 We give an overview of the general framework of forms of Bak, Tits and Wall, when restricting to vector spaces over fields, and describe its relationship to the classical notions of Hermitian, alternating and quadratic forms.
D. Sprehn, Nathalie Wahl
semanticscholar +1 more source
Classes of weak Dembowski–Ostrom polynomials for multivariate quadratic cryptosystems
Journal of Mathematical Cryptology, 2015 T. Harayama and D. K. Friesen [J. Math. Cryptol. 1 (2007), 79–104] proposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski–Ostrom (DO) polynomials in this framework over the finite field 𝔽2.
Alam Bilal, Özbudak Ferruh, Yayla Oğuz
doaj +1 more source
Generalised quadratic forms and the u-invariant [PDF]
, 2017 The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in characteristic 2 and
Dolphin, Andrew
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Quadratic forms and linear algebraic groups [PDF]
, 2009 Topics discussed at the workshop Quadratic Forms and Linear Algebraic Groups included besides the algebraic theory of quadratic and Hermitian forms and their Witt groups several aspects of the theory of linear algebraic groups and homogeneous varieties ...
Harbater, David +2 more
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