T. Ziegler

activity

20022023

most citedUniversal Characteristic Factors and Furstenberg Averages

136 citations · 534 across the 27 of their papers we have counts for

collaborators

31 papers

math.NT2023

Infinite partial sumsets in the primes

Terence Tao, Tamar Ziegler

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 $1 \leq i < j$ .

math.NT2022★ 2 cited

On rank in algebraic closure

Amichai Lampert, Tamar Ziegler

Let $k$ be a field and $Q \in k [x_{1}, \dots, x_{s}]$ a form (homogeneous polynomial) of degree $d > 1.$ The $k$ -Schmidt rank $r k_{k} (Q)$ of $Q$ i…

math.AC2021★ 1 cited

Relative Rank and Regularization

Amichai Lampert, Tamar Ziegler

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…

math.AG2021★ 11 cited

On the Schmidt and analytic ranks for trilinear forms

Karim Adiprasito, David Kazhdan, Tamar Ziegler

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 pro…

math.AG2020

Applications of Algebraic Combinatorics to Algebraic Geometry

David Kazhdan, Tamar Ziegler

We formulate a number of new results in Algebraic Geometry and outline their derivation from Theorem 2.12 which belongs to Algebraic Combinatorics.

math.AG2019★ 4 cited

On the codimension of the singular locus

David Kazhdan, Tamar Ziegler

Let $k$ be a field and $V$ an $k$ -vector space. For a family $P ˉ = {P_{i}}_{1 \leq i \leq c},$ of polynomials on $V$ , we denote by $X_{P ˉ} \subset V$ the subscheme de…

math.AG2019

Properties of high rank subvarieties of affine spaces

David Kazhdan, Tamar Ziegler

We use tools of additive combinatorics for the study of subvarieties defined by {\it high rank} families of polynomials in high dimensional $F_{q}$ -vector spaces. In the fi…

math.AG2018★ 3 cited

Extending weakly polynomial functions from high rank varieties

David Kazhdan, Tamar Ziegler

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 subsp…

math.AG2018

On ranks of polynomials

David Kazhdan, Tamar Ziegler

Let $V$ be a vector space over a field $k, P : V \to k, d \geq 3$ . We show the existence of a function $C (r, d)$ such that $r ank (P) \leq C (r, d)$ for any field $k, c ha r (k) > d$ , a finite-d…

math.CO2017★ 4 cited

Extending linear and quadratic functions from high rank varieties

David Kazhdan, Tamar Ziegler

Let $k$ be a field, $V$ be a $k$ -vector space and $X \subset V$ an algebraic irreducible subvariety. We say that a function $f : X (k) \to k$ is weakly linear if its restriction to any…

math.CO2017

Polynomial functions as splines

David Kazhdan, Tamar Ziegler

Let $V$ be a vector space over a finite field $k$ . We give a condition on a subset $A \subset V$ that allows for a local criterion for checking when a function $f : A \to k$ is a res…

math.GR2017

Appoximate Cohomology

David Kazhdan, Tamar Ziegler

Let $k$ be a field, $G$ be an abelian group and $r \in N$ . Let $L$ be an infinite dimensional $k$ -vector space. For any $m \in E n d_{k} (L)$ we denote by $r (m) \in [0, \infty]$ th…

math.NT2017

On the bias of cubic polynomials

David Kazhdan, Tamar Ziegler

Let $V$ be a vector space over a finite field $k = F_{q}$ of dimension $n$ . For a polynomial $P : V \to k$ we define the bias of $P$ to be $$b_1(P)=\frac {|\sum _{v\in V}ψ(P(V))…

math.NT2016★ 4 cited

Polynomial patterns in the primes

Terence Tao, Tamar Ziegler

Let $P_{1}, \dots, P_{k} : Z \to Z$ be polynomials of degree at most $d$ for some $d \geq 1$ , with the degree $d$ coefficients all distinct, and admissible in the sense…

math.CO2016★ 18 cited

Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors

Terence Tao, Tamar Ziegler

We establish a number of "concatenation theorems" that assert, roughly speaking, that if a function exhibits "polynomial" (or "Gowers anti-uniform", "uniformly almost periodic", or…

math.NT2014

Narrow progressions in the primes

Terence Tao, Tamar Ziegler

In a previous paper of the authors, we showed that for any polynomials $P_{1}, \dots, P_{k} \in Z [m]$ with $P_{1} (0) = \dots = P_{k} (0)$ and any subset $A$ of the primes in $[N] = \{1,…

math.NT2014★ 1 cited

Linear equations in primes and dynamics of nilmanifolds

Tamar Ziegler

We survey some of the ideas behind the recent developments in additive number theory, combinatorics and ergodic theory leading to the proof of Hardy- Littlewood type estimates for…

math.NT2013★ 2 cited

A multi-dimensional Szemerédi theorem for the primes via a correspondence principle

Terence Tao, Tamar Ziegler

We establish a version of the Furstenberg-Katznelson multi-dimensional Szemerédi in the primes $P := {2, 3, 5, \dots}$ , which roughly speaking asserts that any dense sub…

math.DS2013★ 1 cited

Multiple recurrence and convergence results associated to $F_{p}^{ω}$ -actions

Vitaly Bergelson, Terence Tao, Tamar Ziegler

Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of $F_{p}^{ω}$ . From this…

math.NT2011

Distjointness of Mobius from horocycle flows

Jean Bourgain, Peter Sarnak, Tamar Ziegler

We formulate and prove a finite version of Vinogradov's bilinear sum inequality. We use it together with Ratner's joinings theorems to prove that the Mobius function is disjoint fr…

math.CO2011★ 5 cited

The inverse conjecture for the Gowers norm over finite fields in low characteristic

Terence Tao, Tamar Ziegler

We establish the \emph{inverse conjecture for the Gowers norm over finite fields}, which asserts (roughly speaking) that if a bounded function $f: V \to \C$ on a finite-dimensional…

math.CO2010★ 12 cited

An inverse theorem for the Gowers U^{s+1}[N]-norm

Ben Green, Terence Tao, Tamar Ziegler

We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s<3 have also been previously established. More precisely, we es…

math.DS2010★ 17 cited

The shifted primes and the multidimensional Szemeredi and polynomial van der Waerden theorems

Vitaly Bergelson, Alexander Leibman, Tamar Ziegler

In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes.

math.NT2010★ 15 cited

An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement)

Ben Green, Terence Tao, Tamar Ziegler

In this note we announce the proof of the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s => 3; this is new for s => 4, the cases s = 1,2,3 having been previously estab…

Infinite partial sumsets in the primes

On rank in algebraic closure

Relative Rank and Regularization

On the Schmidt and analytic ranks for trilinear forms

Applications of Algebraic Combinatorics to Algebraic Geometry

On the codimension of the singular locus

Properties of high rank subvarieties of affine spaces

Extending weakly polynomial functions from high rank varieties

On ranks of polynomials

Extending linear and quadratic functions from high rank varieties

Polynomial functions as splines

Appoximate Cohomology

On the bias of cubic polynomials

Polynomial patterns in the primes

Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors

Narrow progressions in the primes

Linear equations in primes and dynamics of nilmanifolds

A multi-dimensional Szemerédi theorem for the primes via a correspondence principle

Multiple recurrence and convergence results associated to Fpω​-actions

Distjointness of Mobius from horocycle flows

The inverse conjecture for the Gowers norm over finite fields in low characteristic

An inverse theorem for the Gowers U^{s+1}[N]-norm

The shifted primes and the multidimensional Szemeredi and polynomial van der Waerden theorems

An inverse theorem for the Gowers U^{s+1}[N]-norm (announcement)

Multiple recurrence and convergence results associated to $F_{p}^{ω}$ -actions