Zobrazeno 1 - 10
of 110
pro vyhledávání: '"Ziegler, Tamar"'
The (low soundness) linearity testing problem for the middle slice of the Boolean cube is as follows. Let $\varepsilon>0$ and $f$ be a function on the middle slice on the Boolean cube, such that when choosing a uniformly random quadruple $(x,y,z ,x\o
Externí odkaz:
http://arxiv.org/abs/2402.05217
Autor:
Tao, Terence, Ziegler, Tamar
Publikováno v:
Journal d'Analyse Math\'ematique Volume 151, pages 375--389, (2023)
We show that there exist infinite sets $A = \{a_1,a_2,\dots\}$ and $B = \{b_1,b_2,\dots\}$ of natural numbers such that $a_i+b_j$ is prime whenever $1 \leq i < j$.
Comment: 13 pages, no figures. A reference has been corrected
Comment: 13 pages, no figures. A reference has been corrected
Externí odkaz:
http://arxiv.org/abs/2301.10303
Autor:
Lampert, Amichai, Ziegler, Tamar
Publikováno v:
Sel. Math. New Ser. 30, 15 (2024)
Let $ {\mathbf k} $ be a field and $Q\in {\mathbf k}[x_1, \ldots, x_s]$ a form (homogeneous polynomial) of degree $d>1.$ The ${\mathbf k}$-Schmidt rank $rk_{\mathbf k}(Q)$ of $Q$ is the minimal $r$ such that $Q= \sum_{i=1}^r R_iS_i$ with $R_i, S_i \i
Externí odkaz:
http://arxiv.org/abs/2205.05329
Autor:
Lampert, Amichai, Ziegler, Tamar
We introduce a new concept of rank - relative rank associated to a filtered collection of polynomials. When the filtration is trivial our relative rank coincides with Schmidt rank (also called strength). We also introduce the notion of relative bias.
Externí odkaz:
http://arxiv.org/abs/2106.03933
We discuss relations between different notions of ranks for multilinear forms. In particular we show that the Schmidt and the analytic ranks for trilinear forms are essentially proportional.
Externí odkaz:
http://arxiv.org/abs/2102.03659
Publikováno v:
Ann. of Math. (2), 197 (2), 739-857, 2023
Let $\lambda$ denote the Liouville function. We show that, as $X \rightarrow \infty$, $$\int_{X}^{2X} \sup_{\substack{P(Y)\in \mathbb{R}[Y]\\ deg(P)\leq k}} \Big | \sum_{x \leq n \leq x + H} \lambda(n) e(-P(n)) \Big |\ dx = o ( X H)$$ for all fixed $
Externí odkaz:
http://arxiv.org/abs/2007.15644
Autor:
Kazhdan, David, Ziegler, Tamar
We formulate a number of new results in Algebraic Geometry and outline their derivation from Theorem 2.12 which belongs to Algebraic Combinatorics.
Comment: Added several applications
Comment: Added several applications
Externí odkaz:
http://arxiv.org/abs/2005.12542
Autor:
Kazhdan, David, Ziegler, Tamar
Let $k$ be a field and $V$ an $k$-vector space. For a family $\bar P=\{ P_i\}_{1\leq i\leq c}, $ of polynomials on $V$, we denote by $\mathbb X _{\bar P}\subset V$ the subscheme defined by the ideal generated by $ \bar P$. We show the existence of $\
Externí odkaz:
http://arxiv.org/abs/1907.11750
Autor:
Kazhdan, David, Ziegler, Tamar
We use tools of additive combinatorics for the study of subvarieties defined by {\it high rank} families of polynomials in high dimensional $\mathbb{F} _q$-vector spaces. In the first, analytic part of the paper we prove a number properties of high r
Externí odkaz:
http://arxiv.org/abs/1902.00767
Autor:
Kazhdan, David, Ziegler, Tamar
Let $k$ be a field, $V$ a $k$-vector space and $X$ be a subset of $V $. A function $f:X\to k$ is weakly polynomial of degree $\leq a$, if the restriction of $f$ on any affine subspace $L\subset X$ is a polynomial of degree $\leq a$. In this paper we
Externí odkaz:
http://arxiv.org/abs/1808.09439