Habibur Rahaman

collaborators

4 papers

math.NT2025

Diophantine approximation with sums of two squares II

Stephan Baier, Habibur Rahaman

Recently, the authors showed that for every irrational number $α$ , there exist infinitely many positive integers $n$ represented by any given positive definite binary quadratic for…

math.NT2025

Diophantine approximation with sums of two squares

Stephan Baier, Habibur Rahaman

For any given positive definite binary quadratic form $Q$ with integer coefficients, we establish two results on Diophantine approximation with integers represented by $Q$ . Firstly…

math.NT2024

Primes and polygonal numbers

Soumya Bhattacharya, Habibur Rahaman

A linear combination $a T_{r} (m) + b T_{s} (n)$ of an \mbox{ $r$ -gonal} number $T_{r} (m)$ and an $s$ -gonal number $T_{s} (n)$ with mutually coprime positive integer coefficients $a$ and $b$ produ…

math.NT2024

Diophantine Approximation with Piatetski-Shapiro Primes

Stephan Baier, Habibur Rahaman

We prove that for every irrational number $α$ , real number $β$ , real number $c$ satisfying $1 < c < 9/8$ and positive real number $θ$ satisfying $θ < (9/ c - 8) /10$ , there exist infinitely…