Linear independence of non-constant zero-constant-term polynomials determines syndeticity and A-IP* property of large-return sets R_ε and their combinatorial analogs S_ε in ergodic theory and Banach density.
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2026 2verdicts
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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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Sets of large values of polynomial multi-correlation functions
Linear independence of non-constant zero-constant-term polynomials determines syndeticity and A-IP* property of large-return sets R_ε and their combinatorial analogs S_ε in ergodic theory and Banach density.
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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.