Representing an element in F_q[t] as the sum of two irreducibles in F_{q^{s}}[t]

Details Representing an element in F_q[t] as the sum of two irreducibles in F_{q^{s}}[t] Representing an element in F_q[t] as the sum of two irreducibles in F_{q^{s}}[t]

2008-09-25

arxiv.org/abs/0809.4381v1

Mathematics

Number Theory

10 pages

Scientific paper

A monic polynomial in F_q[t] of degree n over a finite field F_q of odd
characteristic can be written as the sum of two irreducible monic elements in
F_{q^{s}}[t] of degrees n and n-1 if s is sufficiently large. Such a
representation is possible in F_q[t] if q is larger than an explicitly given
bound in terms of n.

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