Abstract In 2008, Klemm–Pandharipande defined Gopakumar–Vafa type invariants of a
Calabi–Yau 4-folds using Gromov–Witten theory. Recently, Cao–Maulik–Toda proposed a …

The number of lattice points in d-dimensional hyperbolic or elliptic shells {m: a< Q [m]< b},
which are restricted to rescaled and growing domains r Ω, is approximated by the volume …

We establish effective versions of Oppenheim's conjecture for generic inhomogeneous
quadratic forms. We prove such results for fixed shift vectors and generic quadratic forms …

Let H denote a connected component of a stratum of translation surfaces. We show that the
Siegel-Veech transform of a bounded compactly supported function on R< sup> 2 is in L< …

Using results from spectral theory of Eisenstein series, we prove a formula for the second
moment of the Siegel transform when averaged over the subspace of symplectic lattices …

arXiv:1606.02388v1 [math.NT] 8 Jun 2016 Page 1 arXiv:1606.02388v1 [math.NT] 8 Jun 2016
A QUANTITATIVE OPPENHEIM THEOREM FOR GENERIC TERNARY QUADRATIC FORMS …

We formulate and prove the extension of the Rogers integral formula (Rogers [Acta Math. 94
(1955), 249–287]) to the adeles of number fields. We also prove the second moment …

We prove effective versions of Oppenheim's conjecture for generic inhomogeneous forms in
the S‐arithmetic setting. We prove an effective result for fixed rational shifts and generic …

We establish that the optimal bound for the size of the smallest integral solution of the
Oppenheim Diophantine approximation problem $| Q (x)-\\xi|<\\epsilon $ for a generic …

We study the light-cone Siegel transform, transforming functions on the light cone of a
rational indefinite quadratic form Q to a function on the homogenous space SO Q+(Z)﹨ SO …