{"id":{"repo_id":"missouri","oai_identifier":"oai:mospace.umsystem.edu:10355/44166"},"canonical_url":"https://search.dev.ndltd.org/etd/missouri/oai:mospace.umsystem.edu:10355/44166","repository":{"repo_id":"missouri","name":"University of Missouri","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Irrational behavior of algebraic discrete valuations","abstract":"[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI-COLUMBIA AT AUTHOR'S REQUEST.] We construct a family of algebraic discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasi-polynomial and a bounded function. We further show that the set of multiplicities associated to these algebraic discrete rank 1 valuations contains the interval [0, 1/8 ). In particular, the associated multiplicites can be irrational.","abstract_html":"[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI-COLUMBIA AT AUTHOR'S REQUEST.] We construct a family of algebraic discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasi-polynomial and a bounded function. We further show that the set of multiplicities associated to these algebraic discrete rank 1 valuations contains the interval [0, 1/8 ). In particular, the associated multiplicites can be irrational.","abstract_has_math":false,"creators":["Sanyal, Soumya Deepta"],"institution":"University of Missouri--Columbia","degree_name":"Ph. D.","degree_level":"Doctoral","degree_discipline":"Mathematics (MU)","degree_department":null,"school":null,"contributors":[],"advisors":["Cutkosky, Steven Dale"],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-24T03:07:35Z","subjects":["Author supplied: valuation; irrational; multiplicity; Hilbert Function"],"languages":["eng","English"],"rights":["Access to files is limited to the University of Missouri--Columbia with SSO login."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.32469/10355/44166"],"render_values":[{"text":"https://doi.org/10.32469/10355/44166","href":"https://doi.org/10.32469/10355/44166","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10355/44166","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Cutkosky, Steven Dale"]},{"key":"dc:creator","label":"Author","values":["Sanyal, Soumya Deepta"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-11-06T21:50:43Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-11-06T21:50:43Z"]},{"key":"dc:date.issued","label":"Date","values":["2014"]},{"key":"dc:publisher","label":"Institution","values":["University of Missouri--Columbia"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics (MU)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. 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We further show that the set of multiplicities associated to these algebraic discrete rank 1 valuations contains the interval [0, 1/8 ). In particular, the associated multiplicites can be irrational."]},{"key":"dc:title","label":"Title","values":["Irrational behavior of algebraic discrete valuations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Cutkosky, Steven Dale"],"dc:creator":["Sanyal, Soumya Deepta"],"dc:date.accessioned":["2014-11-06T21:50:43Z"],"dc:date.available":["2014-11-06T21:50:43Z"],"dc:date.issued":["2014"],"dc:description":["\"May 2014.\"","Dissertation supervisor: Professor Steven Dale Cutkosky.","Includes vita."],"dc:description.abstract":["[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI-COLUMBIA AT AUTHOR'S REQUEST.] We construct a family of algebraic discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasi-polynomial and a bounded function. We further show that the set of multiplicities associated to these algebraic discrete rank 1 valuations contains the interval [0, 1/8 ). In particular, the associated multiplicites can be irrational."],"dc:identifier.doi":["https://doi.org/10.32469/10355/44166"],"dc:identifier.uri":["https://hdl.handle.net/10355/44166"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["University of Missouri--Columbia"],"dc:rights":["Access to files is limited to the University of Missouri--Columbia with SSO login."],"dc:subject":["Author supplied: valuation; irrational; multiplicity; Hilbert Function"],"dc:title":["Irrational behavior of algebraic discrete valuations"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics (MU)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["University of Missouri--Columbia"]},"updated_at":"2026-07-24T03:07:35Z"}