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<Article>
<Journal>
				<PublisherName>Iranian Mathematical Society (IMS)</PublisherName>
				<JournalTitle>Bulletin of the Iranian Mathematical Society</JournalTitle>
				<Issn>1017-060X</Issn>
				<Volume>37</Volume>
				<Issue>No. 4</Issue>
				<PubDate PubStatus="epublish">
					<Year>2011</Year>
					<Month>12</Month>
					<Day>15</Day>
				</PubDate>
			</Journal>
<ArticleTitle>Upper bounds on the solutions to n = p+m^2</ArticleTitle><FirstPage>95</FirstPage>
			<LastPage>108</LastPage>
			<Language>en</Language>
<AuthorList>
<Author>
					<FirstName>A. </FirstName>
					<LastName>Nayebi</LastName>
					<Affiliation></Affiliation>
				</Author>
</AuthorList>
			<History>
				<PubDate PubStatus="received">
					<Year>2010</Year>
					<Month>01</Month>
					<Day>16</Day>
				</PubDate>
			</History>
		<Abstract><![CDATA[ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is an integer, and $left(frac{n}{p}right)$ denotes the Legendre symbol. Unfortunately, as we will later point out, this conjecture is difficult to prove and not emph{all} integers that are nonsquares can be represented as the sum of a prime and a square. Instead in this paper we prove two upper bounds for $mathcal{R}(n)$ for $n le N$. The first upper bound applies to emph{all} $n le N$. The second upper bound depends on the possible existence of the Siegel zero, and assumes its existence, and applies to all $N/2 < n le N$ but at most $ll N^{1-delta_1}$ of these integers, where $N$ is a sufficiently large positive integer and $0]]></Abstract>
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			<Param Name="value">Conjecture H</Param>
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			<Object Type="keyword">
			<Param Name="value">circle method</Param>
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