19 citations · 56 across the 16 of their papers we have counts for
17 papers
The Fully Inhomogeneous -Adic Littlewood Conjecture
Menny Aka, Alexander Gorodnik, Pankaj Vishe +1
We prove that for almost every , the \textit{fully inhomogeneous -adic Littlewood Conjecture} holds; namely, $$\forall\, δ\in\mathbb{R},\;\forall\, κ\in\mathbb{Z…
Effective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$
Andreas Strömbergsson, Anders Södergren, Pankaj Vishe
Let $G=\SL(2,\R)\ltimes(\R^2)^{k}$, let be a congruence subgroup of $\SL(2,\Z)\ltimes(\Z^2)^{k}$, and let be the one-parameter subgroup of given by…
A two-dimensional delta symbol method and its application to pairs of quadratic forms
Junxian Li, Simon L. Rydin Myerson, Pankaj Vishe
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 ap…
Rational curves on complete intersections and the circle method
Tim Browning, Pankaj Vishe, Shuntaro Yamagishi
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 spr…
On the Hasse principle for complete intersections
Matthew Northey, Pankaj Vishe
We prove the Hasse principle for a smooth projective variety $X\subset \PP^{n-1}_\Q$ defined by a system of two cubic forms as long as . The main tool here is the d…
A sparse equidistribution result for
Pankaj Vishe
Let , let , where is a co-compact lattice in , let be a non-singular quadratic form and let…
Rational points on complete intersections over
Pankaj Vishe
A Kloosterman refinement for function fields is developed and used to establish the quantitative arithmetic of the set of rational points on a smooth complete i…
An effective equidistribution result for and application to inhomogeneous quadratic forms
Andreas Strömbergsson, Pankaj Vishe
Let SL and let be a congruence subgroup of SL. We prove a polynomially effective asymptotic equidistribution res…
On the Hasse principle for quartic hypersurfaces
Oscar Marmon, Pankaj Vishe
We establish the Hasse principle for smooth projective quartic hypersurfaces of dimension greater than or equal to 28 defined over .
Rational curves on smooth hypersurfaces of low degree
Tim Browning, Pankaj Vishe
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.
Simultaneous Diophantine approximation - logarithmic improvements
Alexander Gorodnik, Pankaj Vishe
This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed…
Rational points on cubic hypersurfaces over
Tim Browning, Pankaj Vishe
For any finite field k of characteristic exceeding 3, the Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field k(t),…
Rational curves on smooth cubic hypersurfaces over finite fields
Tim Browning, Pankaj Vishe
Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least…
Uniform bounds for period integrals and sparse equidistribution
James Tanis, Pankaj Vishe
Let be a compact manifold, and let be a function of zero average. We use spectral methods to get uniform (i.e. independ…
Cubic hypersurfaces and a version of the circle method for number fields
Tim Browning, Pankaj Vishe
A version of the Hardy-Littlewood circle method is developed for number fields K/Q and is used to show that non-singular projective cubic hypersurfaces over K always have a K-ratio…
A Fast Algorithm to Compute l(1/2, f x χ_q)
Pankaj Vishe
Let be a fixed (holomorphic or Maass) modular cusp form. Let $\cq$ be a Dirichlet character mod . We describe a fast algorithm that computes the value up…
Rapid computation of L-functions for modular forms
Pankaj Vishe
Let be a fixed (holomorphic or Maass) modular cusp form, with -function . We describe an algorithm that computes the value to any specified precision…