Geodesic
Sums of Three Prime Squares
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 549-558.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Let $A, \epsilon > 0$ be arbitrary. Suppose that $x$ is a sufficiently large positive number. We prove that the number of integers $n \in (x, x+x^\theta]$, satisfying some natural congruence conditions, which cannot be written as the sum of three squares of primes is $\ll x^\theta(\log x)^{-A}$, provided that $\frac{7}{16} + \epsilon \leq \theta \leq 1$.
Siano $A, \epsilon > 0$ arbitrari. Supponiamo che $x$ sia un numero positivo sufficientemente grande. Proviamo che il numero di interi $n$ appartenenti ad $(x, x+x^\theta]$, e soddisfacenti alcune condizioni di congruenza naturali, che non si possono scrivere come somma di tre quadrati di primi è $\ll x^\theta(\log x)^{-A}$ con $\frac{7}{16}+ \epsilon \leq \theta \leq 1$. 
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Mikawa, Hiroshi; Peneva, Temenoujka. Sums of Three Prime Squares. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 549-558. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a3/

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