Refine your search
Collections
Co-Authors
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Zaharescu, Alexandru
- An ABC Analog for Arithmetical Functions
Abstract Views :159 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL-61801, US
1 Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL-61801, US
Source
Journal of the Ramanujan Mathematical Society, Vol 25, No 4 (2010), Pagination: 345-354Abstract
In this paper we state and prove an analog of the abc conjecture in the ring Ar (K) of arithmetical functions in r variables over a field K of characteristic zero.- A Class of Irreducible Polynomials
Abstract Views :281 |
PDF Views:0
Authors
Affiliations
1 “Ovidius” University of Constanta, Bd. Mamaia 124, 8700, Constanta, RO
2 Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, RO
3 Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, IL, 61801, US
1 “Ovidius” University of Constanta, Bd. Mamaia 124, 8700, Constanta, RO
2 Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, RO
3 Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, IL, 61801, US
Source
Journal of the Ramanujan Mathematical Society, Vol 17, No 3 (2002), Pagination: 161–172Abstract
For any polynomial
f (X) ∈ Q[X], write f (X) in the form f(x) =a0+a1X+....+adXd / q
with q,a0,a1,......,aad ∈ Z,q > 1,q as small as possible, then set
H(f) = max{|a0|,|a1|,......,|ad|,q}
we show that for any relatively prime polynomials f(x), g(x) ∈ Q[X] with deg f < deg g = d, and any prime number p>2dd H(f)d+1 H(g)3d, the polynomial f(X) + pg(X) is irreducible over Q. we also condider the more general case of polynomial defined over a number field.