• Corpus ID: 236169743

Decoupling inequalities for short generalized Dirichlet sequences

  title={Decoupling inequalities for short generalized Dirichlet sequences},
  author={Yu Fu and Larry Guth and Dominique Maldague},
We study decoupling theory for functions on R with Fourier transform supported in a neighborhood of short Dirichlet sequences {log n} 1/2 n=N+1 , as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression. 

Figures from this paper

Partial sums of typical multiplicative functions over short moving intervals

. We prove that the k -th positive integer moment of partial sums of Steinhaus random multiplicative functions over the interval ( x, x + H ] matches the corresponding Gaussian moment, as long as H ≪



Ten lectures on the interface between analytic number theory and harmonic analysis

Uniform distribution van der Corput sets Exponential sums I: The methods of Weyl and van der Corput Exponential sums II: Vinogradov's method An introduction to Turan's method Irregularities of

On the multilinear restriction and Kakeya conjectures

We prove d-linear analogues of the classical restriction and Kakeya conjectures in Rd. Our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of

Fourier Restriction, Decoupling, and Applications

This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain–Guth induction on scales and the polynomial method.

Improved decoupling for the parabola

We prove an $(l^2, l^6)$ decoupling inequality for the parabola with constant $(\log R)^c$. In the appendix, we present an application to the six-order correlation of the integer solutions to

Incidence Estimates for Well Spaced Tubes

We prove analogues of the Szemeredi-Trotter theorem and other incidence theorems using $\delta$-tubes in place of straight lines, assuming that the $\delta$-tubes are well-spaced in a strong sense.

Topics in Multiplicative Number Theory

Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value

On Falconer’s distance set problem in the plane

If $$E \subset \mathbb {R}^2$$ E ⊂ R 2 is a compact set of Hausdorff dimension greater than 5 / 4, we prove that there is a point $$x \in E$$ x ∈ E so that the set of distances $$\{ |x-y| \}_{y \in

Combinatorial Complexity of Convex Sequences

The proof is based on weighted incidence theory and an inductive procedure which allows us to deal with higher-dimensional interactions effectively and is borrowed from [CES+] where much of the higher- dimensional incidence theoretic motivation comes from.