## 2009 Number Theory Seminar - 11

- Date: 04/02/2009

Lecturer(s):
Shanta Laishram (University of Waterloo)

Location:

University of British Columbia

Topic:

Irreducibility of generalised Hermite-Laguerre polynomials

Description:

Let a, a_0, a_1, ..., a_m be integers with a nonnegative, and define

f_a(x) = sum_{j=0}^m a_j x^j / (j+a)!. Schur (in 1929) proved that

f_0(x) with |a_0| = |a_n| = 1 is irreducible for all m. Schur's result

has been generalized by many authors by using p-adic methods of Coleman

and Filaseta. In this talk, I will give a survey of the some of these

results and prove some results on the irreducibility of generalised

Hermite-Laguerre polynomials by combining p-adic methods with the

greatest prime factor of the product of terms of an arithmetic

progression.

Schedule:

3:00pm-3:50pm, WMAX 216