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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.NT2018
Uniform subconvexity and symmetry breaking reciprocity
Valentin Blomer, Rizwanur Khan
A non-symmetric reciprocity formula is established that expresses the fourth moment of automorphic L-functions of level q and primitive central character twisted by the l-th Hecke…
math.NT2018
The fifth moment of Hecke L-functions in the weight aspect
Rizwanur Khan
We prove an upper bound for the fifth moment of Hecke L-functions associated to holomorphic Hecke cusp forms of full level and weight k in a dyadic interval K < k < 2K, as K tends…