• Corpus ID: 236169743

Decoupling inequalities for short generalized Dirichlet sequences

@inproceedings{Fu2021DecouplingIF,
  title={Decoupling inequalities for short generalized Dirichlet sequences},
  author={Yu Fu and Larry Guth and Dominique Maldague},
  year={2021}
}
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. 

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References

SHOWING 1-10 OF 13 REFERENCES
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
TLDR
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
TLDR
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.
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