Sums of Three Prime Squares

Mikawa, Hiroshi; Peneva, Temenoujka

Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 549-558 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

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 $\frac{7}{16}+\epsilon\leq\theta\leq 1$ .

Publié le : 2007-10-01

MR 2351527 | Zbl 1177.11086

@article{BUMI_2007_8_10B_3_549_0,
     author = {Hiroshi Mikawa and Temenoujka Peneva},
     title = {Sums of Three Prime Squares},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {549-558},
     zbl = {1177.11086},
     mrnumber = {2351527},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_549_0}
}

Mikawa, Hiroshi; Peneva, Temenoujka. Sums of Three Prime Squares. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 549-558. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_549_0/

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