Average order of an arithmetic function: Difference between revisions

Revision as of 05:13, 1 April 2023

Revision as of 05:14, 1 April 2023

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<math display="block">D(n)=x \log_q(x)+x</math> which resembles closely the analogous result for integers <math display="inline">\sum_{k=1}^n d(k) = x\log x+(2\gamma-1) x + O(\sqrt{x})</math>, where <math>\gamma</math> is [[Euler constant]].

Not much is known about the error term for the integers, while in the polynomials case, there is no error term. This is because of the very simple nature of the zeta function <math>\zeta_{A}(s)</math>, and that it has NOno zeros.

====Polynomial von Mangoldt function====