4 papers · 1 filter
Arithmetic sensitivity of cumulant growth in lacunary sums: transcendental versus algebraic ratio limits
Christoph Aistleitner, Zakhar Kabluchko, Joscha Prochno
We study the asymptotic behavior of cumulants of lacunary trigonometric sums , , and show that cumulant growth is highly sens…
A sharp threshold for arithmetic effects on the tail probabilities of lacunary sums
Christoph Aistleitner, Lorenz Fruehwirth, Joscha Prochno
A classical observation in analysis asserts that lacunary systems of dilated functions show many properties which are also typical for systems of independent random variables. For…
On the behavior of the colored Jones polynomial of the figure-eight knot under modular transformations
Christoph Aistleitner, Manuel Hauke
The colored Jones polynomial is an important quantum knot invariant in low-dimensional topology. In his seminal paper on quantum modular forms, Zagier predicted the behav…
Almost sure asymptotics for the number variance of dilations of integer sequences
Christoph Aistleitner, Nadav Yesha
Let be a sequence of integers. We study the number variance of dilations modulo 1 in intervals of length , and establish pseudorandom…