Results 1 
7 of
7
The Irreducibility Of The Bessel Polynomials
"... this paper, we resolve this conjecture and establish the following generalization. ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
this paper, we resolve this conjecture and establish the following generalization.
On The Irreducibility Of The Generalized Laguerre Polynomials
 Acta Arith
, 2000
"... this paper is to establish the following: ..."
Shorey’s influence in the theory of irreducible polynomials
 in: N. Saradha (Ed.), Diophantine Equations, Narosa Publ
, 2008
"... Dedicated to Tarlok N. Shorey and his continuing contributions to Number Theory ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Dedicated to Tarlok N. Shorey and his continuing contributions to Number Theory
Generalizations of some irreducibility results by Schur
, 2009
"... Let a ≥ 0 and a0, a1,...,an be integers with ..."
ALGEBRAIC PROPERTIES OF A FAMILY OF GENERALIZED LAGUERRE POLYNOMIALS
, 2008
"... Abstract. We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the parameter. For integers r, n ≥ 0, we conjecture that L (−1−n−r) n (x) = ∑n () n−j+r j j=0 n−j x /j! is a Qirreducible polynomial whose Galois group contains the alternating group on n ..."
Abstract
 Add to MetaCart
Abstract. We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the parameter. For integers r, n ≥ 0, we conjecture that L (−1−n−r) n (x) = ∑n () n−j+r j j=0 n−j x /j! is a Qirreducible polynomial whose Galois group contains the alternating group on n letters. That this is so for r = n was conjectured in the 50’s by Grosswald and proven recently by Filaseta and Trifonov. It follows from recent work of Hajir and Wong that the conjecture is true when r is large with respect to n ≥ 5. Here we verify it in three situations: i) when n is large with respect to r, ii) when r ≤ 8, and iii) when n ≤ 4. The main tool is the theory of padic Newton Polygons.
IRREDUCIBILITY CRITERIA FOR SUMS OF TWO RELATIVELY PRIME POLYNOMIALS
"... Abstract. We provide irreducibility conditions for polynomials of the form f(X)+p k g(X), with f and g relatively prime polynomials with integer coefficients, deg f < deg g, p a prime number and k a positive integer. In particular, we prove that if k is prime to deg g − deg f and p k exceeds a certa ..."
Abstract
 Add to MetaCart
Abstract. We provide irreducibility conditions for polynomials of the form f(X)+p k g(X), with f and g relatively prime polynomials with integer coefficients, deg f < deg g, p a prime number and k a positive integer. In particular, we prove that if k is prime to deg g − deg f and p k exceeds a certain bound depending on the coefficients of f and g, then f(X)+p k g(X) is irreducible over Q. 1.