Irreducible polynomials in F_q[x] versus 1 - qz in C[z]

Details Irreducible polynomials in F_q[x] versus 1 - qz in C[z] Irreducible polynomials in F_q[x] versus 1 - qz in C[z]

2006-12-20

arxiv.org/abs/math/0612614v3

Mathematics

Number Theory

2 pages. v.1 replaced because the proof of absolute convergence was valid only on reals. (It used l'Hopital.) Sadder news: "..

Scientific paper

Let q be a prime power and N_n count degree-n monic irreducible polynomials
in F_q[x]. We show that prod_{n=1}^{\infty} (1 -z^n)^N_n = 1 - qz for small
|z|.

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