3 papers
math.NT2026
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…
math.DS2026
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…
math.AG2024
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…