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.
One Citation
Partial sums of typical multiplicative functions over short moving intervals
- Mathematics, Computer Science
- 2022
We show that properly normalized partial sums of typical multiplicative functions arising from realizations of random multiplicative functions have Gaussian limiting distribution in short moving…
References
SHOWING 1-10 OF 13 REFERENCES
Ten lectures on the interface between analytic number theory and harmonic analysis
- Mathematics
- 1994
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
- Mathematics
- 2005
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
- Mathematics
- 2019
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
- Mathematics
- 2020
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
- MathematicsGeometric and Functional Analysis
- 2019
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
- Mathematics
- 1971
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
- MathematicsInventiones mathematicae
- 2019
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
- MathematicsDiscret. Comput. Geom.
- 2006
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.