A variable coefficient multi-frequency lemma
Shaoming Guo, Pavel Zorin-Kranich
TL;DR
This paper extends Bourgain's multi-frequency lemma to variable coefficients, enabling improved major arc estimates for certain discrete operators related to Stein--Wainger type problems.
Contribution
It introduces a variable coefficient version of Bourgain's multi-frequency lemma, advancing the analysis of discrete Stein--Wainger operators.
Findings
Provides a new lemma applicable to variable coefficients
Enables better major arc estimates for specific discrete operators
Contributes to harmonic analysis and number theory techniques
Abstract
We show a variable coefficient version of Bourgain's multi-frequency lemma. It can be used to obtain major arc estimates for a discrete Stein--Wainger type operator considered by Krause arXiv:1803.09431 and Roos arXiv:1907.00405.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Spectral Theory in Mathematical Physics