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

Showing math.NTShow all

10 papers · 1 filter

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.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.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.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.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…

math.NT2006★ 133 cited

The primes contain arbitrarily long polynomial progressions

Terence Tao, Tamar Ziegler

We establish the existence of infinitely many \emph{polynomial} progressions in the primes; more precisely, given any integer-valued polynomials $P_1, >..., P_k \in \Z[\m]$ in one…