Bourbaki

Exercise 10, § 2

Algebra, IV, p. 88

It is set in small type as supplementary.

Let ff be a non-zero element of Z[X1,...,Xn]Z[X_1, ..., X_n]. Let N(q)N(q) be the number of zeros off in the cell ∣x1∣≤q,...,∣xn∣≤q|x_1| \leq q, ..., |x_n| \leq q. Then N(q)/qnN(q)/q^n tends to 0 as q→+∞q \to + \infty.

Solution

No solution has been written yet.

Transcribed from the printed volume. Not translated.