Affine curve of an absolutely irreducible polynomialLet f ∈ F q [ X , Y...

Howard Nelson

Howard Nelson

Answered

2022-11-22

Affine curve of an absolutely irreducible polynomial
Let f F q [ X , Y ] be an absolutely irreducible polynomial of degree n. Denote the affine curve defined by the equation f ( X , Y ) = 0 over F q by Γ ( F q ), and let d = deg Γ. The for each m there exists q 0 such that | Γ ( F q ) | m for all q q 0 .

Answer & Explanation

Kaeden Lara

Kaeden Lara

Expert

2022-11-23Added 23 answers

Step 1
It is trivial as we have the inequality | Γ ( F q ) | q + 1 + ( d 1 ) ( d 2 ) q dStep 2
Now q + 1 grows faster than ( d 1 ) ( d 2 ) q d

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