Divyum Sharma

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20162025

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5 papers · 1 filter

math.NT2025

Explicit and Mixed Estimates for Thue inequalities with few coefficients

N. Saradha, Divyum Sharma

Let $F (x, y)$ be an irreducible form of degree $r \geq 3$ and having $s + 1$ non-zero coefficients. Let $h \geq 1$ be an integer and consider the Thue inequality $∣ F (x, y) ∣ \leq h .$ Fol…

math.NT2024

On the representation of an integer in Ostrowski and recurrence numeration systems

Mohit Mittal, Divyum Sharma

We provide an effective upper bound for positive integers with bounded Hamming weights with respect to both a linear recurrence numeration system and an Ostrowski- $α$ numeration sy…

math.NT2022

Diagonalizable Thue Equations -- revisited

N. Saradha, Divyum Sharma

Let $r, h \in N$ with $r \geq 7$ and let $F (x, y) \in Z [x, y]$ be a binary form such that \[ F(x , y) =(αx + βy)^r -(γx + δy)^r, \] where $α$ , $β$ , $γ$ and $δ$ are alge…

math.NT2017

Joint distribution in residue classes of the base- $q$ and Ostrowski digital sums

Divyum Sharma

Let $q$ be an integer $\geq 2$ and let $S_{q} (n)$ denote the sum of digits of $n$ in base $q$ . For \[ α=[0;\overline{1,m}],\ m\geq 2, \] let $S_{α} (n)$ denote the sum of digits in the…

math.NT2016

Contributions to a conjecture of Mueller and Schmidt on Thue inequalities

N. Saradha, Divyum Sharma

Let $F (X, Y) = i = 0 \sum s a_{i} X^{r_{i}} Y^{r - r_{i}} \in Z [X, Y]$ be a form of degree $r = r_{s} \geq 3$ , irreducible over $Q$ and having at most $s + 1$ non-zero coefficient…

Explicit and Mixed Estimates for Thue inequalities with few coefficients

On the representation of an integer in Ostrowski and recurrence numeration systems

Diagonalizable Thue Equations -- revisited

Joint distribution in residue classes of the base-q and Ostrowski digital sums

Contributions to a conjecture of Mueller and Schmidt on Thue inequalities

Joint distribution in residue classes of the base- $q$ and Ostrowski digital sums