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.
Frantzikinakis,A multidimensional Szemer´ edi theorem for Hardy sequences of different growth, Trans
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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.