An Ω-result related to r4(n).
Résumé
Let r4(n) be the number of ways of writing n as the sum of four squares. Set P4(x)=∑n≤xr4(n)−12π2x2, the error term for the average order of this arithmetical function.
In this paper, following the ideas of Erd\"os and Shapiro, a new elementary method is developed which yields the slightly stronger result P4(x)=Ω+(xloglogx). We also apply our method to give an upper bound for a quantity involving the Euler φ-function. This second result gives an elementary proof of a theorem of H. L. Montgomery
Domaines
Mathématiques [math]Origine | Accord explicite pour ce dépôt |
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