2013/04/08 by Emmanuel Kowalski, Kowalski, Emmanuel, Joseph Najnudel +3 · 1 citation
Mathematics · #Approximation Theory and Sequence Spaces #Mathematical Analysis and Transform Methods #Analytic Number Theory Research
paper · doi:10.48550/arxiv.1304.2179
In this note, we characterize the limiting functions in mod-Gausssian convergence; our approach sheds a new light on the nature of mod-Gaussian convergence as well. Our results in fact more generally apply to mod-* convergence, where * stands for any family of probability distributions whose Fourier transforms do not vanish. We moreover provide new examples, including two new examples of (restricted) mod-Cauchy convergence from arithmetics related to Dedekind sums and the linking number of modular geodesics.