Nilotpal Sinha

collaborators

2 papers

math.GM2026

Asymptotic Formulae For Reciprocal Partitions

Nilotpal Kanti Sinha

For integers $1 \leq m \leq n$ , let $s (n, m)$ denote the number of $m$ -tuples $(k_{1}, \dots, k_{m})$ of nonnegative integers satisfying \[ n=\sum_{j=1}^{m}\frac{k_j}{j}. \] We obtain a comp…

math.GM2026

Chebyshev Bias for Largest Prime Factors

Nilotpal Kanti Sinha

Let $P^{+} (n)$ be the largest prime factor of $n$ , and let $χ = χ_{- 4}$ be $1$ on primes $1 (mod 4)$ and $- 1$ on primes $3 (mod 4)$ . For fixed $k \geq 2$ we study \[ D_k(x)=\sum_{\substack{n\…