Shanta Laishram

activity

20102026

most citedSome irreducibility results for truncated binomial expansions

10 citations · 42 across the 20 of their papers we have counts for

collaborators

Showing 2013Show all

6 papers · 1 filter

math.NT2013★ 1 cited

Grimm's Conjecture and Smooth Numbers

Shanta Laishram, Ram Murty

Let $g (n)$ be the largest positive integer $k$ such that there are distinct primes $p_{i}$ for $1 \leq i \leq k$ so that $p_{i} ∣ n + i$ . This function is related to a celebrated conjecture…

math.NT2013★ 10 cited

Some irreducibility results for truncated binomial expansions

Sudesh K. Khanduja, Ramneek Khassa, Shanta Laishram

For positive integers $n > k$ , let $P_{n, k} (x) = j = 0 \sum k (j n) x^{j}$ be the polynomial obtained by truncating the binomial expansion of $(1 + x)^{n}$ at the $k^{th}…

math.NT2013★ 6 cited

Extensions of Schur's irreducibility results

Shanta Laishram, T. N. Shorey

We prove that the generalised Laguerre polynomials $L_{n}^{(α)} (x)$ with $0\le \al\le 50$ are irreducible except for finitely many pairs $(n, \al)$ and that these exceptions are ne…

math.NT2013★ 7 cited

Irreducibility of generalized Hermite-Laguerre polynomials

Shanta Laishram, T. N. Shorey

For a rational $q = u + \frac{α}{d}$ with $u, α, d\in \ACOBZ$ with $u \geq 0, 1 \leq α < d$ , $g cd (α, d) = 1$ , the \emph{generalized Hermite-Laguerre polynomials $G_{q} (x)$ } are defined by \begin{…

math.NT2013★ 10 cited

Irreducibility of generalized Hermite-Laguerre Polynomials II

Shanta Laishram, T. N. Shorey

In this paper, we show that for each $n \geq 1$ , the generalised Hermite-Laguerre Polynomials $G_{\frac{1}{4}}$ and $G_{\frac{3}{4}}$ are either irreducible or linear polynomial tim…

math.NT2013★ 3 cited

Irreducibility of generalized Hermite-Laguerre Polynomials III

Shanta Laishram, Tarlok Shorey

For a positive integer $n$ and a real number $α$ , the generalized Laguerre polynomials are defined by \begin{align*} L^{(α)}_n(x)=\sum^n_{j=0}\frac{(n+α)(n-1+α)\cdots (j+1+α)(-x)^j…