# Mod-$\phi$ convergence

Delbaen, Freddy; Kowalski, Emmanuel; Nikeghbali, Ashkan (2015). Mod-$\phi$ convergence. International Mathematics Research Notices, 2015(11):3445-3485.

## Abstract

Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex Brownian motion and the classical situation of the central limit theorem, and a conjecture concerning the distribution of values of the Riemann zeta function on the critical line.

## Abstract

Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex Brownian motion and the classical situation of the central limit theorem, and a conjecture concerning the distribution of values of the Riemann zeta function on the critical line.

## Statistics

### Citations

Dimensions.ai Metrics
13 citations in Web of Science®
8 citations in Scopus®

### Altmetrics

Detailed statistics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English June 2015 14 Jan 2016 11:47 08 Oct 2019 07:17 Oxford University Press 1073-7928 Green https://doi.org/10.1093/imrn/rnu035