L. Singhal

activity

20182025

collaborators

3 papers

math.NT2025

Representing an integer and its powers in two unrelated number systems

Divyum Sharma, L. Singhal

Let $α$ be a fixed quadratic irrational. Consider the Diophantine equation \[ y^a\ =\ q_{N_1} + \cdots + q_{N_K},\quad N_1 \geq \cdots \geq N_{K} \geq 0,\quad a, y \geq 2 \] where…

math.NT2019

Inhomogeneous Diophantine approximation over fields of formal power series

Yann Bugeaud, L. Singhal, Zhenliang Zhang

We prove a sharp analogue of Minkowski's inhomogeneous approximation theorem over fields of power series $F_{q} ((T^{- 1}))$ . Furthermore, we study the approximation to a give…

math.DS2018

Cylinder absolute games on solenoids

L. Singhal

Let $A$ be any affine surjective endomorphism of a solenoid $Σ_{P}$ over the circle $S^{1}$ which is not an infinite-order translation of $Σ_{P}$ . We prove the ex…