Prime geodesic theorem for the Picard manifold

2018/04/01 by Balkanova, Olga, Frolenkov, Dmitry · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1804.00275

Abstract

Let Γ=PSL(2,Z[i]) be the Picard group and H³ be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient Γ∖ H³, called the Picard manifold, obtaining an error term of size O(X^3/2+θ/2+ε), where θ denotes a subconvexity exponent for quadratic Dirichlet L-functions defined over Gaussian integers.

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• The hyperbolic lattice counting problem in large dimensions

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