Sums of Three Prime Squares

Mikawa, Hiroshi, and Peneva, Temenoujka. "Sums of Three Prime Squares." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 549-558. <http://eudml.org/doc/290367>.

@article{Mikawa2007,
abstract = {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 $\frac\{7\}\{16\} + \epsilon \leq \theta \leq 1$.},
author = {Mikawa, Hiroshi, Peneva, Temenoujka},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {549-558},
publisher = {Unione Matematica Italiana},
title = {Sums of Three Prime Squares},
url = {http://eudml.org/doc/290367},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Mikawa, Hiroshi
AU - Peneva, Temenoujka
TI - Sums of Three Prime Squares
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 549
EP - 558
AB - 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 $\frac{7}{16} + \epsilon \leq \theta \leq 1$.
LA - eng
UR - http://eudml.org/doc/290367
ER -