5 papers
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…
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 , wh…
The bad and rough rotation is Poissonian
Manuel Hauke
Motivated by the Berry-Tabor Conjecture and the seminal work of Rudnick-Sarnak, the fine-scale properties of sequences with $(a_n)_{n \in \mathbb…
Limit laws for cotangent and Diophantine sums
Bence Borda, Lorenz Frühwirth, Manuel Hauke
Limit laws for ergodic averages with a power singularity over circle rotations were first proved by Sinai and Ulcigrai, as well as Dolgopyat and Fayad. In this paper, we prove limi…
On a Problem of Kac concerning Anisotropic Lacunary Sums
Lorenz Fruehwirth, Manuel Hauke
Given a lacunary sequence , arbitrary positive weights that satisfy a Lindeberg-Feller condition, and a function $f: \mathbb{T}…