Outputs (2)

Rational points on cubic hypersurfaces over F(q,t) (2015)
Journal Article
Browning, T., & Vishe, P. (2015). Rational points on cubic hypersurfaces over F(q,t). Geometric And Functional Analysis, 25(3), 671-732. https://doi.org/10.1007/s00039-015-0328-5

The Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field Fq(t)Fq(t), provided that char (Fq)>3(Fq)>3 and X has dimension at least 6.

Uniform Bounds for Period Integrals and Sparse Equidistribution (2015)
Journal Article
Tanis, J., & Vishe, P. (2015). Uniform Bounds for Period Integrals and Sparse Equidistribution. International Mathematics Research Notices, 2015(24), 13728-13756. https://doi.org/10.1093/imrn/rnv115

Let M=Γ∖PSL(2,R) be a compact manifold, and let f∈C∞(M) be a function of zero average. We use spectral methods to get uniform (i.e., independent of spectral gap) bounds for twisted averages of f along long horocycle orbit segments. We apply this to o... Read More about Uniform Bounds for Period Integrals and Sparse Equidistribution.