By John Knopfmacher Wen-Bin Zhang

ISBN-10: 0585412286

ISBN-13: 9780585412283

ISBN-10: 0824705777

ISBN-13: 9780824705770

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**Example text**

13 of [AB], £ n(a) 9(a)<7V £ [n

1 and the equation d2*(y) = {Z (y)]4 / Z ( y 2 ) . 5) PROPOSITION. of degree N is The average value of d2(a) for elements a G Q }]-lNz + O(N2) as N -> oo. 6) PROPOSITION. The average value of (3 for dements of degree N in Q is if V = |, ifv>\. 5: Error estimates for ... PROOF. We have /3#(y) = Z ( y ) g # ( y } , where g # ( y ) = Z(y^Z(y3}/Z(y6}. Then g*(y] = Z(y2)h*(y), where h*(y) = Z ( y 3 ) / Z ( y 6 ) is absolutely convergent for \y\ < q~z. Hence g(N) = since h f ( q ~ ? ) is absolutely convergent.

1 below, for example), attention may and normally will be confined to specifying the asymptotic behaviour of the relevant numbers f ( N ) as N —> oo, since the same denominator G(N] appears throughout and is given asymptotically by Axiom A*. -l implies that = £ /(«)- £ 7H n

### Number Theory Arising from Finite Fields by John Knopfmacher Wen-Bin Zhang

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