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Southeastern Regional Meeting on Numbers (SERMON)
May 2-3, 1998
University of North Carolina at Greensboro
Greensboro, NC, USA |
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Organizers
Theresa P. Vaughan, Robert T. Johnson
View Abstracts
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The irreducibility of the Bessel polynomials
by
Michael Filaseta
University of South Carolina
Coauthors: Ognian Trifonov
In 1951, Grosswald investigated the irreducibility over the rationals
of the Bessel polynomials
|
yn(x) = |
n
å
j=0
|
|
(n+j)!
2j (n-j)! j!
|
xj |
|
and conjectured that yn(x) is irreducible for every positive integer n.
Using Newton polygons and precise analytic formulas in the distribution of
prime numbers, the speaker and Ognian Trifonov have resolved
the conjecture. The talk will focus on describing how these ideas lead
to a proof that all Bessel polynomials are irreducible and discuss
related results concerning the irreducibility of other classical polynomials.
Date received: April 16, 1998
Copyright © 1998 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caar-06.