arXiv subjects

Goran Djanković

Publications and source records attributed to Goran Djanković.

3 recordsLinked to original sources

arXiv2024

The fourth moment of truncated Eisenstein series

We obtain an asymptotic for the fourth moment of truncated Eisenstein series of large Laplacian eigenvalue, verifying for the first time that the main term corresponds to Gaussian random behavior. This is a manifestation of the Random Wave Conjecture, which for Eisenstein series was formulated by Hejhal and Rackner over thirty years ago. Our innovation is to tackle the problem after introducing, at no cost, an extra averaging over the truncation parameter.

math.NT↗

arXiv2018

On the Random Wave Conjecture for Eisenstein series

We obtain an asymptotic for the regularized fourth moment of the Eisenstein series for the full modular group, in agreement with the Random Wave Conjecture.

math.NT↗

arXiv2017

A conjecture for the regularized fourth moment of Eisenstein series

We formulate a version of the Random Wave Conjecture for the fourth moment of Eisenstein series which is based on Zagier's regularized inner product. We prove an asymptotic formula expressing the regularized fourth moment as a mean value of L-functions. This is an advantage over previous work in the literature, which has approached the fourth moment problem through truncated Eisenstein series and not yielded a suitable expression in terms of L-functions.

math.NT↗