{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1756"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1756","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"Explicit multiplicative relations between Gauss sums","abstract":"H.Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes.","abstract_html":"H.Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes.","abstract_has_math":false,"creators":["Murray, Brian J."],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2002,"date_issued":"2002-01-01T08:00:00Z","date_published":"2002-01-01T08:00:00Z","updated_at":"2026-07-24T02:58:17Z","subjects":["character sums"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-0708102-134248","https://repository.lsu.edu/gradschool_dissertations/757"],"render_values":[{"text":"etd-0708102-134248","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/757","href":"https://repository.lsu.edu/gradschool_dissertations/757","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.757","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Murray, Brian J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2002-06-25"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:09:53Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["character sums"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-0708102-134248","10.31390/gradschool_dissertations.757","https://repository.lsu.edu/gradschool_dissertations/757"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["H.Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes."]},{"key":"dc:title","label":"Title","values":["Explicit multiplicative relations between Gauss sums"]}]}],"canonical_facts":{"dc:creator":["Murray, Brian J."],"dc:date":["2002-06-25"],"dc:date.available":["2022-05-12T23:09:53Z"],"dc:description.abstract":["H.Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes."],"dc:identifier":["etd-0708102-134248","10.31390/gradschool_dissertations.757","https://repository.lsu.edu/gradschool_dissertations/757"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["character sums"],"dc:title":["Explicit multiplicative relations between Gauss sums"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:58:17Z"}