Duke Mathematical Journal

Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties

Paula B. Cohen

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Abstract

We generalize to Hilbert modular varieties of arbitrary dimension the work of W. Duke [16] on the equidistribution of Heegner points and of primitive positively oriented closed geodesics in the Poincaré upper half-plane, subject to certain subconvexity results. We also prove vanishing results for limits of cuspidal Weyl sums associated with analogous problems for the Siegel upper half-space of degree 2. In particular, these Weyl sums are associated with families of Humbert surfaces in Siegel 3-folds and of modular curves in these Humbert surfaces.

Article information

Source
Duke Math. J., Volume 129, Number 1 (2005), 87-127.

Dates
First available in Project Euclid: 15 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1121448865

Digital Object Identifier
doi:10.1215/S0012-7094-04-12914-8

Mathematical Reviews number (MathSciNet)
MR2153457

Zentralblatt MATH identifier
1155.11326

Subjects
Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms
Secondary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]

Citation

Cohen, Paula B. Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties. Duke Math. J. 129 (2005), no. 1, 87--127. doi:10.1215/S0012-7094-04-12914-8. https://projecteuclid.org/euclid.dmj/1121448865


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