"Riemann-Roch theorem" meaning in English

{
  "etymology_text": "Initially proven by Bernhard Riemann (1857); further work was done by Riemann's student Gustav Roch (1865).",
  "forms": [
    {
      "form": "the Riemann-Roch theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "def": "1"
      },
      "expansion": "the Riemann-Roch theorem",
      "name": "en-prop"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "An important theorem in complex analysis and algebraic geometry for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles."
      ],
      "id": "en-Riemann-Roch_theorem-en-name-G4q7WJAY",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "complex analysis",
          "complex analysis"
        ],
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "computation",
          "computation"
        ],
        [
          "dimension",
          "dimension"
        ],
        [
          "space",
          "space"
        ],
        [
          "meromorphic",
          "meromorphic"
        ],
        [
          "function",
          "function"
        ],
        [
          "zero",
          "zero"
        ],
        [
          "pole",
          "pole"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An important theorem in complex analysis and algebraic geometry for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles."
      ],
      "related": [
        {
          "word": "Weierstrass point"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Bernhard Riemann",
        "Gustav Roch"
      ]
    }
  ],
  "word": "Riemann-Roch theorem"
}

{
  "etymology_text": "Initially proven by Bernhard Riemann (1857); further work was done by Riemann's student Gustav Roch (1865).",
  "forms": [
    {
      "form": "the Riemann-Roch theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "def": "1"
      },
      "expansion": "the Riemann-Roch theorem",
      "name": "en-prop"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "related": [
    {
      "word": "Weierstrass point"
    }
  ],
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English uncountable nouns",
        "en:Mathematics"
      ],
      "glosses": [
        "An important theorem in complex analysis and algebraic geometry for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "complex analysis",
          "complex analysis"
        ],
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "computation",
          "computation"
        ],
        [
          "dimension",
          "dimension"
        ],
        [
          "space",
          "space"
        ],
        [
          "meromorphic",
          "meromorphic"
        ],
        [
          "function",
          "function"
        ],
        [
          "zero",
          "zero"
        ],
        [
          "pole",
          "pole"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An important theorem in complex analysis and algebraic geometry for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Bernhard Riemann",
        "Gustav Roch"
      ]
    }
  ],
  "word": "Riemann-Roch theorem"
}