"Dirichlet character" meaning in All languages combined

{
  "forms": [
    {
      "form": "Dirichlet characters",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Dirichlet character (plural Dirichlet characters)",
      "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": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "1) χ(ab)=χ(a)χ(b);"
        },
        {
          "text": "2) χ(a)=0if; gcd (a,m)>1\\ ne 0if; gcd (a,m)=1. (gcd is the greatest common divisor)"
        },
        {
          "text": "3) χ(a+m)=χ(a)."
        }
      ],
      "glosses": [
        "A complex-valued arithmetic function χ:ℤ→ℂ that satisfies the following conditions for some positive integer m and all integers a and b"
      ],
      "id": "en-Dirichlet_character-en-noun-LmdJKCWE",
      "links": [
        [
          "arithmetic function",
          "arithmetic function"
        ]
      ],
      "raw_glosses": [
        "(analytic number theory) A complex-valued arithmetic function χ:ℤ→ℂ that satisfies the following conditions for some positive integer m and all integers a and b:"
      ],
      "topics": [
        "analytic-number-theory",
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Dirichlet character"
      ]
    }
  ],
  "word": "Dirichlet character"
}

{
  "forms": [
    {
      "form": "Dirichlet characters",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "Dirichlet character (plural Dirichlet characters)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
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      ],
      "examples": [
        {
          "text": "1) χ(ab)=χ(a)χ(b);"
        },
        {
          "text": "2) χ(a)=0if; gcd (a,m)>1\\ ne 0if; gcd (a,m)=1. (gcd is the greatest common divisor)"
        },
        {
          "text": "3) χ(a+m)=χ(a)."
        }
      ],
      "glosses": [
        "A complex-valued arithmetic function χ:ℤ→ℂ that satisfies the following conditions for some positive integer m and all integers a and b"
      ],
      "links": [
        [
          "arithmetic function",
          "arithmetic function"
        ]
      ],
      "raw_glosses": [
        "(analytic number theory) A complex-valued arithmetic function χ:ℤ→ℂ that satisfies the following conditions for some positive integer m and all integers a and b:"
      ],
      "topics": [
        "analytic-number-theory",
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Dirichlet character"
      ]
    }
  ],
  "word": "Dirichlet character"
}