3 papers
math.NT2023
Diophantine Approximation of Anergodic Birkhoff Sums over Rotations
Paul Verschueren
We study Birkhoff sums over rotations (series of the form ), in which the summed function may be unbounded at the origin. Estimates of these sums have been…
math.DS2014
On the growth of Sudler's sine product at the golden rotation number
Paul Verschueren, Ben Mestel
We study the growth at the golden rotation number of Sudler's sine product. This sequence has been variously studied elsewhere as a skew product of sines, Birkhoff sum, q-Pochhamme…
math.DS2013
Fixed points of Composition Sum Operators
Paul Verschueren, Ben D. Mestel
In the renormalisation analysis of critical phenomena in quasi-periodic systems, a fundamental role is often played by fixed points of functional recurrences of the form \begin{equ…