"eigenform" meaning in All languages combined

See eigenform on Wiktionary

Noun [English]

Forms: eigenforms [plural]
Etymology: eigen- + form Etymology templates: {{prefix|en|eigen|form}} eigen- + form Head templates: {{en-noun}} eigenform (plural eigenforms)
  1. (mathematics) A modular form which is an eigenvector for all Hecke operators T_m,m=1,2,3,... Categories (topical): Mathematics
    Sense id: en-eigenform-en-noun-v3gd7HXt Categories (other): English entries with incorrect language header, English terms prefixed with eigen- Topics: mathematics, sciences

Inflected forms

Download JSON data for eigenform meaning in All languages combined (1.7kB)

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  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "eigen",
        "3": "form"
      },
      "expansion": "eigen- + form",
      "name": "prefix"
    }
  ],
  "etymology_text": "eigen- + form",
  "forms": [
    {
      "form": "eigenforms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "eigenform (plural eigenforms)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms prefixed with eigen-",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2015, Yuk-Kam Lau, Emmanuel Royer, Jie Wu, “Sign of Fourier coefficients of modular forms of half integral weight”, in (Please provide the book title or journal name)",
          "text": "We establish lower bounds for (i) the numbers of positive and negative terms and (ii) the number of sign changes in the sequence of Fourier coefficients at squarefree integers of a half-integral weight modular Hecke eigenform.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A modular form which is an eigenvector for all Hecke operators T_m,m=1,2,3,..."
      ],
      "id": "en-eigenform-en-noun-v3gd7HXt",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "modular form",
          "modular form#English"
        ],
        [
          "eigenvector",
          "eigenvector#English"
        ],
        [
          "Hecke operators",
          "Hecke operator#English"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A modular form which is an eigenvector for all Hecke operators T_m,m=1,2,3,..."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "eigenform"
}
{
  "etymology_templates": [
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      "args": {
        "1": "en",
        "2": "eigen",
        "3": "form"
      },
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      "name": "prefix"
    }
  ],
  "etymology_text": "eigen- + form",
  "forms": [
    {
      "form": "eigenforms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "eigenform (plural eigenforms)",
      "name": "en-noun"
    }
  ],
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  "lang_code": "en",
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  "senses": [
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      ],
      "examples": [
        {
          "ref": "2015, Yuk-Kam Lau, Emmanuel Royer, Jie Wu, “Sign of Fourier coefficients of modular forms of half integral weight”, in (Please provide the book title or journal name)",
          "text": "We establish lower bounds for (i) the numbers of positive and negative terms and (ii) the number of sign changes in the sequence of Fourier coefficients at squarefree integers of a half-integral weight modular Hecke eigenform.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A modular form which is an eigenvector for all Hecke operators T_m,m=1,2,3,..."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "modular form",
          "modular form#English"
        ],
        [
          "eigenvector",
          "eigenvector#English"
        ],
        [
          "Hecke operators",
          "Hecke operator#English"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A modular form which is an eigenvector for all Hecke operators T_m,m=1,2,3,..."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "eigenform"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-19 from the enwiktionary dump dated 2024-06-06 using wiktextract (372f256 and 664a3bc). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.