Distribution of cusp sections in the Hilbert modular orbifold

Samuel Estala Arias

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arXiv · 1112.1146

Distribution of cusp sections in the Hilbert modular orbifold

Samuel Estala Arias

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Abstract

Let K be a number field, let M be the Hilbert modular orbifold of K, and let m(q) be the probability measure uniformly supported on the cusp cross sections of M at height q. We generalize a method of Zagier and show that m(q) distributes uniformly with respect to the normalized Haar measure m on M as q tends to zero, and relate the rate by which m(q) approaches m to the Riemann hypothesis for the Dedekind zeta function of K.

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Samuel Estala Arias. 2011-12-06. Distribution of cusp sections in the Hilbert modular orbifold. https://arxiv.org/abs/1112.1146

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