7 papers
Lévy-Khintchine Theorems: effective results and central limit theorems
Gaurav Aggarwal, Anish Ghosh
The Lévy-Khintchine theorem is a classical result in Diophantine approximation that describes the asymptotic growth of the denominators of convergents in the continued fraction ex…
On the packing dimension of weighted singular matrices on fractals
Gaurav Aggarwal, Anish Ghosh
We provide the first known upper bounds for the packing dimension of weighted singular and weighted -singular matrices. We also prove upper bounds for these sets when intersect…
Counting and Joint equidistribution of approximates
Gaurav Aggarwal, Anish Ghosh
In this paper, we consider the problem of counting Diophantine inequalities with multiple natural constraints. We prove a very general result in this setting using dynamical techni…
A survey and a result on inhomogeneous quadratic forms
Sourav Das, Anish Ghosh
We survey recent work done on the values at integer points of irrational inhomogeneous quadratic forms, namely, inhomogeneous analogues of the famous Oppenheim conjecture. We also…
Generalized Lévy-Khintchine Theorems and a Conjecture of Y. Cheung
Gaurav Aggarwal, Anish Ghosh
The celebrated Lévy--Khintchine theorem is a fundamental limiting law that describes the growth rate of the denominators of the convergents in the continued fraction expansion of…
The Doeblin-Lenstra conjecture: effective results and central limit theorems
Gaurav Aggarwal, Anish Ghosh
We establish effective convergence rates in the Doeblin-Lenstra law, describing the limiting distribution of approximation coefficients arising from continued fraction convergents…