17 citations · 73 across the 39 of their papers we have counts for
58 papers
Lacunary sequences in analysis, probability and number theory
Christoph Aistleitner, Istvan Berkes, Robert Tichy
In this paper we present the theory of lacunary trigonometric sums and lacunary sums of dilated functions, from the origins of the subject up to recent developments. We describe th…
On the distribution of partial quotients of reduced fractions with fixed denominator
Christoph Aistleitner, Bence Borda, Manuel Hauke
In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions , where is fixed and runs throu…
On the metric theory of approximations by reduced fractions: a quantitative Koukoulopoulos-Maynard theorem
Christoph Aistleitner, Bence Borda, Manuel Hauke
Let be given. The Duffin-Schaeffer conjecture, recently resolved by Koukoulopoulos and Maynard, asserts that for almost all reals there are infinite…
A conjecture of Zagier and the value distribution of quantum modular forms
Christoph Aistleitner, Bence Borda
In his influential paper on quantum modular forms, Zagier developed a conjectural framework describing the behavior of certain quantum knot invariants under the action of the modul…
Difference sets and the metric theory of small gaps
Christoph Aistleitner, Daniel El-Baz, Marc Munsch
Let be a sequence of distinct positive integers. In a recent paper Rudnick established asymptotic upper bounds for the minimal gaps of $\{a_n α\bmod 1, 1 \leq n…
Maximizing Sudler products via Ostrowski expansions and cotangent sums
Christoph Aistleitner, Bence Borda
There is an extensive literature on the asymptotic order of Sudler's trigonometric product for fixed or for "typical" values of . In th…