Staff profile

• Analytic Number Theory, Homogeneous Dynamics

Journal Article

• On the Hasse Principle For Complete Intersections
  Northey, M. J., & Vishe, P. (2024). On the Hasse Principle For Complete Intersections. Compositio Mathematica, 160(4), 771-835. https://doi.org/10.1112/S0010437X23007698
• Rational points on complete intersections over 𝔽𝒒(𝒕)
  Vishe, P. (2023). Rational points on complete intersections over 𝔽𝒒(𝒕). Proceedings of the London Mathematical Society, 126(2), 556-619. https://doi.org/10.1112/plms.12496
• A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$
  Vishe, P. (2022). A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$. Transactions of the American Mathematical Society, 375(1), 669-694. https://doi.org/10.1090/tran/8498
• An effective equidistribution result for SL(2,R)\ltimes (R^2)^{oplus k} and application to inhomogeneous quadratic forms
  Strombergsson, A., & Vishe, P. (2020). An effective equidistribution result for SL(2,R)\ltimes (R^2)^{oplus k} and application to inhomogeneous quadratic forms. Journal of the London Mathematical Society, 102(1), 143-204. https://doi.org/10.1112/jlms.12316
• On the Hasse Principle for quartic hypersurfaces
  Marmon, O., & Vishe, P. (2019). On the Hasse Principle for quartic hypersurfaces. Duke Mathematical Journal, 168(14), 2722-2729. https://doi.org/10.1215/00127094-2019-0025
• Rational curves on smooth hypersurfaces of low degree
  Browning, T., & Vishe, P. (2017). Rational curves on smooth hypersurfaces of low degree. Algebra & Number Theory, 11(7), 1657-1675. https://doi.org/10.2140/ant.2017.11.1657
• Diophantine approximation for products of linear maps—logarithmic improvements
  Gorodnik, A., & Vishe, P. (2016). Diophantine approximation for products of linear maps—logarithmic improvements. Transactions of the American Mathematical Society, 370(1), 487-507. https://doi.org/10.1090/tran/6953
• Rational points on cubic hypersurfaces over F(q,t)
  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
• Uniform Bounds for Period Integrals and Sparse Equidistribution
  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
• Cubic hypersurfaces and a version of the circle method for number fields
  Browning, T., & Vishe, P. (2014). Cubic hypersurfaces and a version of the circle method for number fields. Duke Mathematical Journal, 163(10), 1825-1883. https://doi.org/10.1215/00127094-2738530
• A fast algorithm to compute L(1/2, f x X(q))
  Vishe, P. (2013). A fast algorithm to compute L(1/2, f x X(q)). Journal of Number Theory, 133(5), https://doi.org/10.1016/j.jnt.2012.10.005