3 papers
math.NT2024
The fourth moment of truncated Eisenstein series
Goran Djanković, Rizwanur Khan
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…
math.NT2018
On the Random Wave Conjecture for Eisenstein series
Goran Djanković, Rizwanur Khan
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.NT2017
A conjecture for the regularized fourth moment of Eisenstein series
Goran Djanković, Rizwanur Khan
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…