Kanigowski, Adam and Lemańczyk, Mariusz and Radziwiłł, Maksym (2020) Prime number theorem for analytic skew products. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210825-184533695
![]() |
PDF
- Submitted Version
See Usage Policy. 1MB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20210825-184533695
Abstract
We establish a prime number theorem for all uniquely ergodic, analytic skew products on the 2-torus T². More precisely, for every irrational α and every 1-periodic real analytic g : R → R of zero mean, let T_(α,g) : T² → T² be defined by (x,y) → x+α ,y+g(x)). We prove that if T_(α,g) is uniquely ergodic then, for every (x,y) ∈ T², the sequence {T^p_(α,g)(x,y)} is equidistributed on T² as p traverses prime numbers. This is the first example of a class of natural, non-algebraic and smooth dynamical systems for which a prime number theorem holds. We also show that such a prime number theorem does not necessarily hold if g is only continuous on T².
Item Type: | Report or Paper (Discussion Paper) | ||||||
---|---|---|---|---|---|---|---|
Related URLs: |
| ||||||
Record Number: | CaltechAUTHORS:20210825-184533695 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210825-184533695 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 110528 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | George Porter | ||||||
Deposited On: | 26 Aug 2021 14:38 | ||||||
Last Modified: | 26 Aug 2021 14:38 |
Repository Staff Only: item control page