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  1. No Access

    Article

    Infinite partial sumsets in the primes

    We show that there exist infinite sets A = (a1, a2, …} and B = {b1, b2, …} of natural numbers such that ai + bj is prime whenever 1 ≤ i < j.

    Terence Tao, Tamar Ziegler in Journal d'Analyse Mathématique (2023)

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    Article

    Optimal Sine and Sawtooth Inequalities

    We determine the optimal inequality of the form \(\sum _{k=1}^m a_k\sin kx\le 1\) ...

    Louis Esser, Terence Tao, Burt Totaro… in Journal of Fourier Analysis and Applicatio… (2022)

  3. Article

    Finite Time Blowup for Lagrangian Modifications of the Three-Dimensional Euler Equation

    In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as ...

    Terence Tao in Annals of PDE (2016)

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    Article

    Multiple recurrence and convergence results associated to \({\text{F}}_P^\omega \) -actions

    Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of ...

    Vitaly Bergelson, Terence Tao, Tamar Ziegler in Journal d'Analyse Mathématique (2015)

  5. No Access

    Article

    Large values of the Gowers-Host-Kra seminorms

    The Gowers uniformity norms \({\left\| f \right\|_{{U^k}(G)}}\) of a function f: G → C on a finite ad...

    Tanja Eisner, Terence Tao in Journal d'Analyse Mathématique (2012)

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    Article

    A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal lemma

    We introduce a correspondence principle (analogous to the Furstenberg Correspondence Principle) that allows one to extract an infinite random graph or hypergraph from a sequence of increasingly large determini...

    Terence Tao in Journal d'Analyse Mathématique (2007)

  7. No Access

    Article

    The Gaussian primes contain arbitrarily shaped constellations

    We show that the Gaussian primesP[i] ⊆ ℤ[i] contain infinitely constellations of any prescribed shape and orientation. More precisely, we show that given any distinct Gaussian integersv 0,...

    Terence Tao in Journal d’Analyse Mathématique (2006)

  8. No Access

    Article

    Uniform estimates on paraproducts

    We prove uniformL p estimates (Theorem 1.1) for a family of paraproducts and corresponding maximal operators.

    Camil Muscalu, Terence Tao, Christoph Thiele in Journal d'Analyse Mathématique (2002)

  9. No Access

    Article

    A physical space approach to wave equation bilinear estimates

    Bilinear estimates for the wave equation in Minkowski space are normally proven using the Fourier transform and Plancherel’s theorem. However, such methods are difficult to carry over to non-flat situations (s...

    Sergiu Klainerman, Igor Rodnianski, Terence Tao in Journal d'Analyse Mathématique (2002)

  10. No Access

    Article

    Uniform estimates on multi-linear operators with modulation symmetry

    In a previous paper [20] in this series, we gaveL p estimates for multi-linear operators given by multipliers which are singular on a non-degenerate subspace of some dimensionk. In this pa...

    Camil Muscalu, Terence Tao, Christoph Thiele in Journal d’Analyse Mathématique (2002)

  11. No Access

    Article

    New bounds for Kakeya problems

    We establish new estimates on the Minkowski and Hausdorff dimensions of Kakeya sets and we obtain new bounds on the Kakeya maximal operator.

    NetsHawk Katz, Terence Tao in Journal d'Analyse Mathématique (2002)