10 citations · 28 across the 8 of their papers we have counts for
10 papers
Extension of Irreducibility results on Generalised Laguerre Polynomials
Saranya G Nair, Tarlok Nath Shorey
We consider the irreducibility of Generalised Laguerre Polynomials for negative integral values given by $L_n^{(-1-n-s)}(x)=\displaystyle\sum_{j=0}^{n}\binom{n-j+s}{n-j}\frac{x^j}{…
Extension of Laguerre polynomials with negative arguments
T. N. Shorey, Sneh Bala Sinha
We consider the irreducibility of polynomial where is a negative integer. We observe that the constant term of vanishes if and only if $n \geq…
Irreducibility of extensions of Laguerre Polynomials
Shanta Laishram, Saranya G. Nair, Tarlok Nath Shorey
For integers with and either with or with , we prove that $ψ_n^{(α)}(x;a_0,a_1,\cdots…
On the Galois group of Generalised Laguerre polynomials II
Shanta Laishram, Saranya G. Nair, Tarlok Nath Shorey
For real number 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…
Arithmetic properties of blocks of consecutive integers
Tarlok N. Shorey, Rob Tijdeman
This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a…
Extensions of Schur's irreducibility results
Shanta Laishram, T. N. Shorey
We prove that the generalised Laguerre polynomials with $0\le \al\le 50$ are irreducible except for finitely many pairs $(n, \al)$ and that these exceptions are ne…
Irreducibility of generalized Hermite-Laguerre polynomials
Shanta Laishram, T. N. Shorey
For a rational with $u, α, d\in \ACOBZ$ with , , the \emph{generalized Hermite-Laguerre polynomials } are defined by \begin{…
Irreducibility of generalized Hermite-Laguerre Polynomials II
Shanta Laishram, T. N. Shorey
In this paper, we show that for each , the generalised Hermite-Laguerre Polynomials and are either irreducible or linear polynomial tim…
Irreducibility of generalized Hermite-Laguerre Polynomials III
Shanta Laishram, Tarlok Shorey
For a positive integer and a real number , 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…
Baker's Explicit abc-Conjecture and applications
Shanta Laishram, T. N. Shorey
The conjecture of Masser-Oesterlé, popularly known as -conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures.