A Fourier-free combinatorial proof of Roth's theorem via density increments on sub-progressions.
Furstenberg,Ergodic behavior of diagonal measures and a theorem of Szemer´ edi on arithmetic progressions, J
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Counterexamples demonstrate that integer-coefficient derivative-span conditions fail to imply thickness or non-emptiness of common return-time sets for recurrence along Hardy field functions.
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A Fourier-Free Density-Increment Proof of Roth's Theorem
A Fourier-free combinatorial proof of Roth's theorem via density increments on sub-progressions.
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Counterexamples to integer-coefficient criteria for recurrence along functions from a Hardy field
Counterexamples demonstrate that integer-coefficient derivative-span conditions fail to imply thickness or non-emptiness of common return-time sets for recurrence along Hardy field functions.