A Higher Order Levin-Fainleib Theorem
Un théorème de Levin-Fainleib d'ordre supérieur
Résumé
When restricted to some non-negative multiplicative function, say f, bounded on primes and that vanishes on non square-free integers, our result provides us with an asymptotic for $\sum_{n\le X}f(n)/n$ with error term $\mathcal{O}((\log X)^{\kappa-h-1+\varepsilon})$ (for any positive $\varepsilon>0$) as soon as we have $\sum_{p\le Q}f(p)(\log p)/p=\kappa\log Q+\eta+\mathcal{O}(1/(\log 2Q)^h)$ for a non-negative $\kappa$ and some non-negative integer h. The method generalizes the 1967-approach of Levin and Fainleib and uses a differential equation.
Domaines
Théorie des nombres [math.NT]Origine | Fichiers produits par l'(les) auteur(s) |
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