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When subset-sums do not cover all the residues modulo p

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Title: When subset-sums do not cover all the residues modulo p
Authors: Deshouillers, Jean-Marc1 jean-marc.deshouillers@math.u-bordeaux.fr, Freiman, Gregory A.2 grisha@math.tau.ac.il
Source: Journal of Number Theory. Feb2004, Vol. 104 Issue 2, p255. 8p.
Subjects: Inverse problems, Number theory, Prime numbers, Automorphisms
Abstract: Let c>√ of 2. We prove that a subset A of Z/pZ, where p is a prime number, with cardinality larger than cp. We prove that a subset A of Z/pZ, where p is a prime number, with cardinality larger than c√ of p such that its subset sums do not cover Z/pZ has an automorphic image which is rather concentrated; more precisely, there exists s prime to p such that∑lower limit a∈A as/p<1+O(p−1/4 ln p). [Copyright &y& Elsevier]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 11886432
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: When subset-sums do not cover all the residues modulo &lt;f&gt;p&lt;/f&gt;
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  Data: &lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Deshouillers%2C+Jean-Marc%22&quot;&gt;Deshouillers, Jean-Marc&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt;&lt;i&gt; jean-marc.deshouillers@math.u-bordeaux.fr&lt;/i&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Freiman%2C+Gregory+A%2E%22&quot;&gt;Freiman, Gregory A.&lt;/searchLink&gt;&lt;relatesTo&gt;2&lt;/relatesTo&gt;&lt;i&gt; grisha@math.tau.ac.il&lt;/i&gt;
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  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Journal+of+Number+Theory%22&quot;&gt;Journal of Number Theory&lt;/searchLink&gt;. Feb2004, Vol. 104 Issue 2, p255. 8p.
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  Data: &lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Inverse+problems%22&quot;&gt;Inverse problems&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Number+theory%22&quot;&gt;Number theory&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Prime+numbers%22&quot;&gt;Prime numbers&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Automorphisms%22&quot;&gt;Automorphisms&lt;/searchLink&gt;
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Let &lt;f&gt;c&gt;√ of &lt;RCD&gt;2&lt;/RCD&gt;&lt;/rad&gt;&lt;/f&gt;. We prove that a subset &lt;f&gt;&lt;sc&gt;A&lt;/sc&gt;&lt;/f&gt; of &lt;f&gt;&lt;of&gt;Z&lt;/of&gt;/p&lt;of&gt;Z&lt;/of&gt;&lt;/f&gt;, where &lt;f&gt;p&lt;/f&gt; is a prime number, with cardinality larger than &lt;f&gt;c&lt;rad&gt;&lt;RCD&gt;p&lt;/RCD&gt;&lt;/f&gt;. We prove that a subset &lt;f&gt;A&lt;/f&gt; of &lt;f&gt;Z/pZ&lt;/f&gt;, where &lt;f&gt;p&lt;/f&gt; is a prime number, with cardinality larger than &lt;f&gt;c√ of &lt;RCD&gt;p&lt;/RCD&gt;&lt;/f&gt; such that its subset sums do not cover &lt;f&gt;Z/pZ&lt;/f&gt; has an automorphic image which is rather concentrated; more precisely, there exists &lt;f&gt;s&lt;/f&gt; prime to &lt;f&gt;p&lt;/f&gt; such that∑lower limit a∈A &lt;fen&gt;&lt;cp type=&quot;vb&quot; style=&quot;s&quot;&gt;&lt;fen&gt;&lt;cp type=&quot;vb&quot; style=&quot;s&quot;&gt;&lt;NU&gt;as&lt;/NU&gt;/p&lt;cp type=&quot;vb&quot; style=&quot;s&quot;&gt;&lt;/fen&gt;&lt;cp type=&quot;vb&quot; style=&quot;s&quot;&gt;&lt;/fen&gt;&lt;1+O(p−1/4 ln p). [Copyright &amp;y&amp; Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: &lt;i&gt;Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.jnt.2003.08.009
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 8
        StartPage: 255
    Subjects:
      – SubjectFull: Inverse problems
        Type: general
      – SubjectFull: Number theory
        Type: general
      – SubjectFull: Prime numbers
        Type: general
      – SubjectFull: Automorphisms
        Type: general
    Titles:
      – TitleFull: When subset-sums do not cover all the residues modulo <f>p</f>
        Type: main
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            NameFull: Deshouillers, Jean-Marc
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            NameFull: Freiman, Gregory A.
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              Text: Feb2004
              Type: published
              Y: 2004
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              Value: 104
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              Value: 2
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            – TitleFull: Journal of Number Theory
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