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math.CA2019
Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions
Jonathan M. Fraser, Pablo Shmerkin, Alexia Yavicoli
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real line which avoid -approximations of arithmetic progressions. Some of…
math.CA2018
Almost arithmetic progressions in the primes and other large sets
Jonathan M. Fraser
A celebrated and deep result of Green and Tao states that the primes contain arbitrarily long arithmetic progressions. In this note I provide a straightforward argument demonstrati…
math.CA2018
The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra
Jonathan M. Fraser, Kathryn E. Hare, Kevin G. Hare +2
We consider the Assouad spectrum, introduced by Fraser and Yu, along with a natural variant that we call the `upper Assouad spectrum'. These spectra are designed to interpolate bet…