{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:59634"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:59634","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Paramodular forms of degree 2 with particular emphasis on level t = 5","abstract":"This PhD thesis deals with paramodular forms of degree 2 with arbitrary multiplier systems. The presented construction methods are Maaß lifts and Borcherds' products.The goal of this thesis was to determine the algebraic structure of the graded algebra of all paramodular forms of degree 2 with level 5. A reduction process requires the calculation of the algebraic structure of a ring of modular forms with lower degree. As a main result of this thesis we present a method to determine an invariant ring for a polynomial ring modulo a (principal) ideal. This method is examplified by the ring of modular forms of lower degree.Finally we show some structural results for the examined algebra, e.g. the Hilbert series, generators for small weight and four algebraically independent paramodular forms which are candidates for a homogeneous system of parameters. Their degrees match the degrees that are predicted by the Hilbert series.","abstract_html":"This PhD thesis deals with paramodular forms of degree 2 with arbitrary multiplier systems. The presented construction methods are Maaß lifts and Borcherds' products.The goal of this thesis was to determine the algebraic structure of the graded algebra of all paramodular forms of degree 2 with level 5. A reduction process requires the calculation of the algebraic structure of a ring of modular forms with lower degree. As a main result of this thesis we present a method to determine an invariant ring for a polynomial ring modulo a (principal) ideal. This method is examplified by the ring of modular forms of lower degree.Finally we show some structural results for the examined algebra, e.g. the Hilbert series, generators for small weight and four algebraically independent paramodular forms which are candidates for a homogeneous system of parameters. 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The presented construction methods are Maaß lifts and Borcherds' products.The goal of this thesis was to determine the algebraic structure of the graded algebra of all paramodular forms of degree 2 with level 5. A reduction process requires the calculation of the algebraic structure of a ring of modular forms with lower degree. As a main result of this thesis we present a method to determine an invariant ring for a polynomial ring modulo a (principal) ideal. This method is examplified by the ring of modular forms of lower degree.Finally we show some structural results for the examined algebra, e.g. the Hilbert series, generators for small weight and four algebraically independent paramodular forms which are candidates for a homogeneous system of parameters. Their degrees match the degrees that are predicted by the Hilbert series."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University VIII, 136 S. (2004). doi:10.18154/RWTH-CONV-121402 = Aachen, Techn. Hochsch., Diss., 2004"]},{"key":"dc:title","label":"Title","values":["Paramodular forms of degree 2 with particular emphasis on level t = 5"]}]}],"canonical_facts":{"dc:contributor":["Krieg, Aloys"],"dc:coverage":["DE"],"dc:creator":["Marschner, Axel"],"dc:date":["2004"],"dc:description":["This PhD thesis deals with paramodular forms of degree 2 with arbitrary multiplier systems. The presented construction methods are Maaß lifts and Borcherds' products.The goal of this thesis was to determine the algebraic structure of the graded algebra of all paramodular forms of degree 2 with level 5. A reduction process requires the calculation of the algebraic structure of a ring of modular forms with lower degree. As a main result of this thesis we present a method to determine an invariant ring for a polynomial ring modulo a (principal) ideal. This method is examplified by the ring of modular forms of lower degree.Finally we show some structural results for the examined algebra, e.g. the Hilbert series, generators for small weight and four algebraically independent paramodular forms which are candidates for a homogeneous system of parameters. Their degrees match the degrees that are predicted by the Hilbert series."],"dc:identifier":["https://publications.rwth-aachen.de/record/59634","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121402%22"],"dc:language":["eng"],"dc:publisher":["Publikationsserver der RWTH Aachen University"],"dc:relation":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-20050640","info:eu-repo/semantics/altIdentifier/doi/10.18154/RWTH-CONV-121402"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Publikationsserver der RWTH Aachen University VIII, 136 S. (2004). doi:10.18154/RWTH-CONV-121402 = Aachen, Techn. 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