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Representing an integer and its powers in two unrelated number systems
Divyum Sharma, L. Singhal
Let 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…
On the coefficient-choosing game
Divyum Sharma, L. Singhal
Nora and Wanda are two players who choose coefficients of a degree polynomial from some fixed unital commutative ring . Wanda is declared the winner if the polynomial has a…
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 . Furthermore, we study the approximation to a give…
Diophantine exponents for standard linear actions of over discrete rings in
L. Singhal
We give upper and lower bounds for various Diophantine exponents associated with the standard linear actions of on the punctured complex plane $\m…