See analytic number theory in All languages combined, or Wiktionary
{ "head_templates": [ { "args": { "1": "-" }, "expansion": "analytic number theory (uncountable)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Armenian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Number theory", "orig": "en:Number theory", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "coordinate_terms": [ { "word": "algebraic number theory" }, { "word": "computational number theory" }, { "word": "geometry of numbers" }, { "word": "geometric number theory" } ], "derived": [ { "word": "abstract analytic number theory" } ], "examples": [ { "text": "1987, F. X. Gallagher, Applications of Guinand's Formula, A.C. Adolphson, A. Ghosh, J.B. Conrey, R.I. Yager (editors), Analytic Number Theory and Diophantine Problems: Proceedings of a Conference, Birkhäuser, page 135,\nAccording to Weil [22], analytic number theory, which deals with inequalities and asymptotic formulas, is not number theory but analysis." }, { "text": "2002, Chaohua Jia, Kohji Matsumoto (editors), Analytic Number Theory, Kluwer Academic, page ix,\nTalks covered various research fields including analytic number theory, algebraic number theory, modular forms and transcendental number theory." }, { "ref": "2002, Song Y. Yan, Number Theory for Computing, 2nd edition, Springer, page 174:", "text": "Computational number theory, however, studies problems from elementary, algebraic geometric and analytic number theory which require the help of fast computers (particularly vector and parallel systems) and fast algorithms (particularly deterministic polynomial-time algorithms).", "type": "quote" } ], "glosses": [ "A branch of number theory that uses methods from mathematical analysis to solve problems about the integers." ], "id": "en-analytic_number_theory-en-noun-nToo~Hk0", "links": [ [ "mathematics", "mathematics" ], [ "number theory", "number theory" ], [ "mathematical analysis", "mathematical analysis" ], [ "integer", "integer" ] ], "raw_glosses": [ "(mathematics, number theory) A branch of number theory that uses methods from mathematical analysis to solve problems about the integers." ], "tags": [ "uncountable" ], "topics": [ "mathematics", "number-theory", "sciences" ], "translations": [ { "code": "hy", "lang": "Armenian", "roman": "analitik tʻveri tesutʻyun", "sense": "branch of number theory", "word": "անալիտիկ թվերի տեսություն" }, { "code": "de", "lang": "German", "sense": "branch of number theory", "tags": [ "feminine" ], "word": "analytische Zahlentheorie" }, { "code": "it", "lang": "Italian", "sense": "branch of number theory", "tags": [ "feminine" ], "word": "teoria analitica dei numeri" } ], "wikipedia": [ "analytic number theory" ] } ], "word": "analytic number theory" }
{ "coordinate_terms": [ { "word": "algebraic number theory" }, { "word": "computational number theory" }, { "word": "geometry of numbers" }, { "word": "geometric number theory" } ], "derived": [ { "word": "abstract analytic number theory" } ], "head_templates": [ { "args": { "1": "-" }, "expansion": "analytic number theory (uncountable)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "English terms with quotations", "English uncountable nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with Armenian translations", "Terms with German translations", "Terms with Italian translations", "en:Mathematics", "en:Number theory" ], "examples": [ { "text": "1987, F. X. Gallagher, Applications of Guinand's Formula, A.C. Adolphson, A. Ghosh, J.B. Conrey, R.I. Yager (editors), Analytic Number Theory and Diophantine Problems: Proceedings of a Conference, Birkhäuser, page 135,\nAccording to Weil [22], analytic number theory, which deals with inequalities and asymptotic formulas, is not number theory but analysis." }, { "text": "2002, Chaohua Jia, Kohji Matsumoto (editors), Analytic Number Theory, Kluwer Academic, page ix,\nTalks covered various research fields including analytic number theory, algebraic number theory, modular forms and transcendental number theory." }, { "ref": "2002, Song Y. Yan, Number Theory for Computing, 2nd edition, Springer, page 174:", "text": "Computational number theory, however, studies problems from elementary, algebraic geometric and analytic number theory which require the help of fast computers (particularly vector and parallel systems) and fast algorithms (particularly deterministic polynomial-time algorithms).", "type": "quote" } ], "glosses": [ "A branch of number theory that uses methods from mathematical analysis to solve problems about the integers." ], "links": [ [ "mathematics", "mathematics" ], [ "number theory", "number theory" ], [ "mathematical analysis", "mathematical analysis" ], [ "integer", "integer" ] ], "raw_glosses": [ "(mathematics, number theory) A branch of number theory that uses methods from mathematical analysis to solve problems about the integers." ], "tags": [ "uncountable" ], "topics": [ "mathematics", "number-theory", "sciences" ], "wikipedia": [ "analytic number theory" ] } ], "translations": [ { "code": "hy", "lang": "Armenian", "roman": "analitik tʻveri tesutʻyun", "sense": "branch of number theory", "word": "անալիտիկ թվերի տեսություն" }, { "code": "de", "lang": "German", "sense": "branch of number theory", "tags": [ "feminine" ], "word": "analytische Zahlentheorie" }, { "code": "it", "lang": "Italian", "sense": "branch of number theory", "tags": [ "feminine" ], "word": "teoria analitica dei numeri" } ], "word": "analytic number theory" }
Download raw JSONL data for analytic number theory meaning in English (2.8kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.