Second Moment of the Prime Geodesic Theorem for PSL(2, ℤ[i])

2018/12/31 by Chatzakos, Dimitrios, Cherubini, Giacomo, Laaksonen, Niko
#11F72 (Primary) 11M36 #11L05 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1812.11916

Abstract

The remainder E_Γ(X) in the Prime Geodesic Theorem for the Picard group Γ= PSL(2,ℤ[i]) is known to be bounded by O(X^3/2+ε) under the assumption of the Lindelöf hypothesis for quadratic Dirichlet L-functions over Gaussian integers. By studying the second moment of E_Γ(X), we show that on average the same bound holds unconditionally.

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• Prime geodesic theorem for the Picard manifold
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