{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T19:58:21Z","timestamp":1760385501794},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"unspecified","delay-in-days":152,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>We propose an algorithm to verify the<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000097_inline3\" \/><jats:tex-math>$p$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-part of the class number for a number field<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000097_inline4\" \/><jats:tex-math>$K$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, provided<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000097_inline5\" \/><jats:tex-math>$K$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is totally real and an abelian extension of the rational field<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000097_inline6\" \/><jats:tex-math>$\\mathbb{Q}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000097_inline7\" \/><jats:tex-math>$p$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is any prime. On fields of degree 4 or higher, this algorithm has been shown heuristically to be faster than classical algorithms that compute the entire class number, with improvement increasing with larger field degrees.<\/jats:p>","DOI":"10.1112\/s1461157016000097","type":"journal-article","created":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T09:42:47Z","timestamp":1464774167000},"page":"217-228","source":"Crossref","is-referenced-by-count":4,"title":["An application of the -adic analytic class number formula"],"prefix":"10.1112","volume":"19","author":[{"given":"Claus","family":"Fieker","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2016,6,1]]},"reference":[{"key":"S1461157016000097_r15","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-58.1.17"},{"key":"S1461157016000097_r2","first-page":"325","volume-title":"Algorithmic number theory: lattices, number fields, curves and cryptography","volume":"44","author":"Bernstein","year":"2008"},{"key":"S1461157016000097_r6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8489-0"},{"key":"S1461157016000097_r10","doi-asserted-by":"crossref","DOI":"10.1515\/9781400881703","volume-title":"Lectures on p-adic L-functions","volume":"74","author":"Iwasawa","year":"1972"},{"key":"S1461157016000097_r5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02945-9"},{"key":"S1461157016000097_r9","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-08-02169-8"},{"key":"S1461157016000097_r1","doi-asserted-by":"publisher","DOI":"10.1007\/11792086_5"},{"key":"S1461157016000097_r11","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-47.1.18"},{"key":"S1461157016000097_r12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03983-0"},{"key":"S1461157016000097_r13","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-02-01432-1"},{"key":"S1461157016000097_r14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1934-7"},{"key":"S1461157016000097_r8","first-page":"97","article-title":"Calcul du nombre de classes et des unit\u00e9s des extensions ab\u00e9liennes r\u00e9elles de\u00a0Q","volume":"101","author":"Gras","year":"1977","journal-title":"Bull. 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