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polynomial ergodic theorems

Ergodic Theory and Dynamical Systems (1)

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1 results

Prime number theorem for regular Toeplitz subshifts
Part of
- Multiplicative number theory
- Topological dynamics
KRZYSZTOF FRĄCZEK, ADAM KANIGOWSKI, MARIUSZ LEMAŃCZYK
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 4 / April 2022

Published online by Cambridge University Press:

15 February 2021, pp. 1446-1473

Print publication:

April 2022
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We prove that neither a prime nor an l-almost prime number theorem holds in the class of regular Toeplitz subshifts. But when a quantitative strengthening of the regularity with respect to the periodic structure involving Euler’s totient function is assumed, then the two theorems hold.