"Nevanlinna theory" meaning in All languages combined

{
  "etymology_text": "Named after Finnish mathematician Rolf Nevanlinna (1895–1980), who published the theory in 1925.",
  "head_templates": [
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      "expansion": "Nevanlinna theory (uncountable)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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          "name": "Complex analysis",
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      "examples": [
        {
          "text": "A key tool in Nevanlinna theory is the Nevanlinna characteristic, T(r,f), which measures the rate of growth of a meromorphic function.",
          "type": "example"
        },
        {
          "ref": "1992, Ilpo Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, page 1:",
          "text": "Precisely, our aim has been to show how the Nevanlinna theory may be applied to get insight into the properties of solutions of complex differential equations.",
          "type": "quote"
        },
        {
          "ref": "2001, William Cherry, Zhuan Ye, Nevanlinna's Theory of Value Distribution, Springer, page vi:",
          "text": "Motivated by an analogy between Nevanlinna theory and Diophantine approximation theory, discovered independently by C. F. Osgood [Osg 1985] and P. Vojta [Vojt 1987], S. Lang recognized that the careful study of the error term in Nevanlinna'a Second Main Theorem would be of interest in itself.",
          "type": "quote"
        },
        {
          "text": "2010, Paul Vojta, Diophantine Approximation and Nevanlinna theory, Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, Paul Vojta (editors), Arithmetic Geometry: Lectures given at the C.I.M.E. Summer School, Springer, Lecture Notes in Mathematics 2009, page 111,\nBeginning with the work of Osgood [65], it has been known that the branch of complex analysis known as Nevanlinna theory (also called value distribution theory) has many similarities with Roth's theorem on diophantine approximation. […] The circle of ideas has developed further in the last 20 years: Lang's conjecture on sharpening the error term in Roth's was carried over to a conjecture in Nevanlinna theory which was proved in many cases."
        }
      ],
      "glosses": [
        "A part of the theory of meromorphic functions that describes the asymptotic distribution of solutions to the equation ƒ(z) = a, as a varies."
      ],
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      "raw_glosses": [
        "(complex analysis) A part of the theory of meromorphic functions that describes the asymptotic distribution of solutions to the equation ƒ(z) = a, as a varies."
      ],
      "related": [
        {
          "word": "Nevanlinna characteristic"
        }
      ],
      "synonyms": [
        {
          "sense": "part of the theory of meromorphic functions",
          "word": "value-distribution theory"
        }
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "complex-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fr",
          "lang": "French",
          "sense": "part of the theory of meromorphic functions",
          "tags": [
            "feminine"
          ],
          "word": "théorie de Nevanlinna"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "part of the theory of meromorphic functions",
          "tags": [
            "feminine"
          ],
          "word": "Nevanlinna-Theorie"
        }
      ],
      "wikipedia": [
        "Acta Mathematica",
        "Nevanlinna theory",
        "Rolf Nevanlinna"
      ]
    }
  ],
  "word": "Nevanlinna theory"
}

{
  "etymology_text": "Named after Finnish mathematician Rolf Nevanlinna (1895–1980), who published the theory in 1925.",
  "head_templates": [
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Nevanlinna characteristic"
    }
  ],
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        "Terms with French translations",
        "Terms with German translations",
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      "examples": [
        {
          "text": "A key tool in Nevanlinna theory is the Nevanlinna characteristic, T(r,f), which measures the rate of growth of a meromorphic function.",
          "type": "example"
        },
        {
          "ref": "1992, Ilpo Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, page 1:",
          "text": "Precisely, our aim has been to show how the Nevanlinna theory may be applied to get insight into the properties of solutions of complex differential equations.",
          "type": "quote"
        },
        {
          "ref": "2001, William Cherry, Zhuan Ye, Nevanlinna's Theory of Value Distribution, Springer, page vi:",
          "text": "Motivated by an analogy between Nevanlinna theory and Diophantine approximation theory, discovered independently by C. F. Osgood [Osg 1985] and P. Vojta [Vojt 1987], S. Lang recognized that the careful study of the error term in Nevanlinna'a Second Main Theorem would be of interest in itself.",
          "type": "quote"
        },
        {
          "text": "2010, Paul Vojta, Diophantine Approximation and Nevanlinna theory, Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, Paul Vojta (editors), Arithmetic Geometry: Lectures given at the C.I.M.E. Summer School, Springer, Lecture Notes in Mathematics 2009, page 111,\nBeginning with the work of Osgood [65], it has been known that the branch of complex analysis known as Nevanlinna theory (also called value distribution theory) has many similarities with Roth's theorem on diophantine approximation. […] The circle of ideas has developed further in the last 20 years: Lang's conjecture on sharpening the error term in Roth's was carried over to a conjecture in Nevanlinna theory which was proved in many cases."
        }
      ],
      "glosses": [
        "A part of the theory of meromorphic functions that describes the asymptotic distribution of solutions to the equation ƒ(z) = a, as a varies."
      ],
      "links": [
        [
          "complex analysis",
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        ],
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        ],
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        ],
        [
          "asymptotic",
          "asymptotic"
        ],
        [
          "distribution",
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        ]
      ],
      "raw_glosses": [
        "(complex analysis) A part of the theory of meromorphic functions that describes the asymptotic distribution of solutions to the equation ƒ(z) = a, as a varies."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "complex-analysis",
        "mathematics",
        "sciences"
      ],
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        "Acta Mathematica",
        "Nevanlinna theory",
        "Rolf Nevanlinna"
      ]
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  ],
  "synonyms": [
    {
      "sense": "part of the theory of meromorphic functions",
      "word": "value-distribution theory"
    }
  ],
  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "part of the theory of meromorphic functions",
      "tags": [
        "feminine"
      ],
      "word": "théorie de Nevanlinna"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "part of the theory of meromorphic functions",
      "tags": [
        "feminine"
      ],
      "word": "Nevanlinna-Theorie"
    }
  ],
  "word": "Nevanlinna theory"
}