36 citations · 36 across the 10 of their papers we have counts for
10 papers
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 sensitiv…
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…
Moment generating functions and moderate deviation principles for lacunary trigonometric sums
Christoph Aistleitner, Lorenz Frühwirth, Manuel Hauke +1
In a recent paper, Aistleitner, Gantert, Kabluchko, Prochno and Ramanan studied large deviation principles (LDPs) for lacunary trigonometric sums , whe…
On Sequences with Exponentially Distributed Gaps
Christoph Aistleitner, Manuel Hauke, Agamemnon Zafeiropoulos
We disprove a folklore conjecture stating that a sequence in with exponential gap distribution must necessarily be uniformly distributed.
Diophantine conditions in the law of the iterated logarithm for lacunary systems
Christoph Aistleitner, Lorenz Frühwirth, Joscha Prochno
It is a classical observation that lacunary function systems exhibit many properties which are typical for systems of independent random variables. However, it had already been obs…
On functions of bounded variation
Christoph Aistleitner, Florian Pausinger, Anne Marie Svane +1
The recently introduced concept of -variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the ope…
On the uniform distribution modulo 1 of multidimensional LS-sequences
Christoph Aistleitner, Markus Hofer, Volker Ziegler
Ingrid Carbone introduced the notion of so-called LS-sequences of points, which are obtained by a generalization of Kakutani's interval splitting procedure. Under an appropriate ch…
Point sets on the sphere with small spherical cap discrepancy
Christoph Aistleitner, Johann Brauchart, Josef Dick
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discre…