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On ternary Diophantine equations of signature (p, p, 2) over number fields

Isik, Erman; Kara, Yasemin; Ozman, Ekin


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  "@context": "https://schema.org/", 
  "@id": 10545, 
  "@type": "ScholarlyArticle", 
  "creator": [
    {
      "@type": "Person", 
      "affiliation": "Bogazici Univ, Fac Arts & Sci, Dept Math, Istanbul, Turkey", 
      "name": "Isik, Erman"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Bogazici Univ, Fac Arts & Sci, Dept Math, Istanbul, Turkey", 
      "name": "Kara, Yasemin"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Bogazici Univ, Fac Arts & Sci, Dept Math, Istanbul, Turkey", 
      "name": "Ozman, Ekin"
    }
  ], 
  "datePublished": "2020-01-01", 
  "description": "Let K be a totally real number field with narrow class number one and O-K be its ring of integers. We prove that there is a constant B-K depending only on K such that for any prime exponent p > B-K the Fermat type equation x(p) + y(p) = z(2) with x, y, z. O-K does not have certain type of solutions. Our main tools in the proof are modularity, level lowering, and image of inertia comparisons.", 
  "headline": "On ternary Diophantine equations of signature (p, p, 2) over number fields", 
  "identifier": 10545, 
  "image": "https://aperta.ulakbim.gov.tr/static/img/logo/aperta_logo_with_icon.svg", 
  "license": "http://www.opendefinition.org/licenses/cc-by", 
  "name": "On ternary Diophantine equations of signature (p, p, 2) over number fields", 
  "url": "https://aperta.ulakbim.gov.tr/record/10545"
}
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