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 2019Show all

5 papers · 1 filter

math.NT2019

Progress towards a nonintegrality conjecture

Shanta Laishram, Daniel López-Aguayo, Carl Pomerance +1

Given $r \in N$ , define the function $S_{r} : N \to Q$ by $S_{r} (n) = k = 0 \sum n \frac{k}{k + r} (k n)$ . In $2015$ , the secon…

math.NT2019

Irreducibility of extensions of Laguerre Polynomials

Shanta Laishram, Saranya G. Nair, Tarlok Nath Shorey

For integers $a_{0}, a_{1}, \dots, a_{n}$ with $∣ a_{0} a_{n} ∣ = 1$ and either $α = u$ with $1 \leq u \leq 50$ or $α = u + \frac{1}{2}$ with $1 \leq u \leq 45$ , we prove that $ψ_n^{(α)}(x;a_0,a_1,\cdots…

math.NT2019★ 2 cited

Irreducibility and Galois Groups of Generalized Laguerre Polynomials $L_{n}^{(- 1 - n - r)} (x)$

Ankita Jindal, Shanta Laishram, Ritumoni Sarma

We study the algebraic properties of Generalized Laguerre polynomials for negative integral values of a given parameter which is $L_{n}^{(-1-n-r)}(x)= \sum\limits_{j=0}^{n} \binom{…

math.NT2019

On the Galois group of Generalised Laguerre polynomials II

Shanta Laishram, Saranya G. Nair, Tarlok Nath Shorey

For real number $α,$ Generalised Laguerre Polynomials (GLP) is a family of polynomials defined by \begin{align*} L_n^{(α)}(x)=(-1)^n\displaystyle\sum_{j=0}^{n}\binom{n+α}{n-j}\frac…

math.NT2019

On members of Lucas sequences which are products of factorials

Shanta Laishram, Florian Luca, Mark Sias

Here, we show that if ${U_{n}}_{n \geq 0}$ is a Lucas sequence, then the largest $n$ such that $∣ U_{n} ∣ = m_{1}! m_{2}! \dots m_{k}!$ with $1 < m_{1} \leq m_{2} \leq \dots \leq m_{k}$ satisfies $n<3\times 1…

Progress towards a nonintegrality conjecture

Irreducibility of extensions of Laguerre Polynomials

Irreducibility and Galois Groups of Generalized Laguerre Polynomials Ln(−1−n−r)​(x)

On the Galois group of Generalised Laguerre polynomials II

On members of Lucas sequences which are products of factorials

Irreducibility and Galois Groups of Generalized Laguerre Polynomials $L_{n}^{(- 1 - n - r)} (x)$