A refinement of Chang's lemma that adds cosetwise l1 control on correlations outside the large spectrum subspace, producing a localized counting lemma for subsets of finite abelian groups.
arXiv preprint arXiv:2007.03528 , year=
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The paper establishes the existence of positive constants c and c_IP for the IP Szemeredi theorem over finite fields and gives strong quantitative bounds in the special cases of Roth and IP-Roth theorems.
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A strengthening of Chang's lemma
A refinement of Chang's lemma that adds cosetwise l1 control on correlations outside the large spectrum subspace, producing a localized counting lemma for subsets of finite abelian groups.
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On the Furstenberg-Katznelson constant for the IP Szemeredi theorem over finite fields
The paper establishes the existence of positive constants c and c_IP for the IP Szemeredi theorem over finite fields and gives strong quantitative bounds in the special cases of Roth and IP-Roth theorems.