Duke Mathematical Journal
- Duke Math. J.
- Volume 129, Number 1 (2005), 87-127.
Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties
We generalize to Hilbert modular varieties of arbitrary dimension the work of W. Duke  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.
Duke Math. J., Volume 129, Number 1 (2005), 87-127.
First available in Project Euclid: 15 July 2005
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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