{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T03:01:17Z","timestamp":1768618877757,"version":"3.49.0"},"reference-count":27,"publisher":"Wiley","issue":"A","license":[{"start":{"date-parts":[[2016,8,26]],"date-time":"2016-08-26T00:00:00Z","timestamp":1472169600000},"content-version":"unspecified","delay-in-days":238,"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 compute the complete set of candidates for the zeta function of a K<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000140_inline4\"\/><jats:tex-math>$3$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>surface over<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000140_inline5\"\/><jats:tex-math>$\\mathbb{F}_{2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>consistent with the Weil and Tate conjectures, as well as the complete set of zeta functions of smooth quartic surfaces over<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000140_inline6\"\/><jats:tex-math>$\\mathbb{F}_{2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. These sets differ substantially, but we do identify natural subsets which coincide. This gives some numerical evidence towards a Honda\u2013Tate theorem for transcendental zeta functions of K<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000140_inline7\"\/><jats:tex-math>$3$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>surfaces; such a result would refine a recent theorem of Taelman, in which one must allow an uncontrolled base field extension.<\/jats:p>","DOI":"10.1112\/s1461157016000140","type":"journal-article","created":{"date-parts":[[2016,8,26]],"date-time":"2016-08-26T15:30:01Z","timestamp":1472225401000},"page":"1-11","source":"Crossref","is-referenced-by-count":6,"title":["A census of zeta functions of quartic K surfaces over"],"prefix":"10.1112","volume":"19","author":[{"given":"Kiran S.","family":"Kedlaya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew V.","family":"Sutherland","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2016,8,26]]},"reference":[{"key":"S1461157016000140_r19","first-page":"53","volume-title":"1969 Number theory institute","author":"Milne","year":"1971"},{"key":"S1461157016000140_r15","doi-asserted-by":"publisher","DOI":"10.24033\/asens.2264"},{"key":"S1461157016000140_r10","unstructured":"10. 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