Shanta Laishram

most citedIrreducibility and Galois Groups of Generalized Laguerre Polynomials

L_{n}^{(- 1 - n - r)} (x)

2 citations · 3 across the 3 of their papers we have counts for

collaborators

7 papers

math.NT2020★ 1 cited

On members of Lucas sequences which are either products of factorials or product of middle binomial coefficients and Catalan numbers

Shanta Laishram

Let ${U_{n}}_{n \geq 0}$ be a Lucas sequence. Then the equation $∣ U_{n} ∣ = m_{1}! m_{2}! \dots m_{k}!$ with $1 < m_{1} \leq m_{2} \leq \dots \leq m_{k}$ implies $n \in {1, 2, 3, 4, 6, 8, 12}$ . Further…

math.NT2020

On members of Lucas sequences which are products of Catalan numbers

Shanta Laishram, Florian Luca, Mark Sias

We show that if ${U_{n}}_{n \geq 0}$ is a Lucas sequence, then the largest $n$ such that $∣ U_{n} ∣ = C_{m_{1}} C_{m_{2}} \dots C_{m_{k}}$ with $1 \leq m_{1} \leq m_{2} \leq \dots \leq m_{k}$ , where $C_m…

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…

On members of Lucas sequences which are either products of factorials or product of middle binomial coefficients and Catalan numbers

On members of Lucas sequences which are products of Catalan numbers

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

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