Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Vishe, Pankaj"'
We present a two-dimensional delta symbol method that facilitates a version of the Kloosterman refinement of the circle method, addressing a question posed by Heath-Brown. As an application, we establish the asymptotic formula for the number of integ
Externí odkaz:
http://arxiv.org/abs/2411.11355
We study the geometry of the space of rational curves on smooth complete intersections of low degree, which pass through a given set of points on the variety. The argument uses spreading out to a finite field, together with an adaptation to function
Externí odkaz:
http://arxiv.org/abs/2404.11123
Autor:
Northey, Matthew, Vishe, Pankaj
We prove the Hasse principle for a smooth projective variety $X\subset \PP^{n-1}_\Q$ defined by a system of two cubic forms $F,G$ as long as $n\geq 39$. The main tool here is the development of a version of Kloosterman refinement for a smooth system
Externí odkaz:
http://arxiv.org/abs/2112.11303
Autor:
Vishe, Pankaj
Let $G=\mathrm{SL}(2,\mathbb{R})^n$, let $\Gamma=\Gamma_0^n$, where $\Gamma_0$ is a co-compact lattice in $\mathrm{SL}(2,\mathbb{R})$, let $F(\mathbf{x})$ be a non-singular quadratic form and let $u(x_1,...,x_n)$ denote the unipotent elements in $G$
Externí odkaz:
http://arxiv.org/abs/2006.08462
Autor:
Vishe, Pankaj
A Kloosterman refinement for function fields $K=\mathbb{F}_q(t)$ is developed and used to establish the quantitative arithmetic of the set of rational points on a smooth complete intersection of two quadrics $X\subset \mathbb{P}^{n-1}_{K}$ , under th
Externí odkaz:
http://arxiv.org/abs/1907.07097
Autor:
Strömbergsson, Andreas, Vishe, Pankaj
Let $G=$SL$(2,R)\ltimes(R^2)^{\oplus k}$ and let $\Gamma$ be a congruence subgroup of SL$(2,Z)\ltimes(Z^2)^{\oplus k}$. We prove a polynomially effective asymptotic equidistribution result for special types of unipotent orbits in $\Gamma\backslash G$
Externí odkaz:
http://arxiv.org/abs/1811.10340
Autor:
Marmon, Oscar, Vishe, Pankaj
Publikováno v:
Duke Math. J. 168, no. 14 (2019), 2727-2799
We establish the Hasse principle for smooth projective quartic hypersurfaces of dimension greater than or equal to 28 defined over $\mathbb{Q}$.
Comment: 50 pages, 1 figure, revision
Comment: 50 pages, 1 figure, revision
Externí odkaz:
http://arxiv.org/abs/1712.07594
Akademický článek
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Autor:
Browning, Tim, Vishe, Pankaj
Publikováno v:
Alg. Number Th. 11 (2017) 1657-1675
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.
Comment: 19 pages; this article replaces arXiv:1502.05028
Comment: 19 pages; this article replaces arXiv:1502.05028
Externí odkaz:
http://arxiv.org/abs/1611.00553