For an imaginary quadratic field $K$ of discriminant $-D$, let $\\chi = \\chi_K$ be the associated quadratic character. We will show that the space of special hermitian Jacobi forms of level $N$ is isomorphic to the space of plus forms of level $DN$ and nebentypus $\\chi$ (the hermitian analogue of Kohnen's plus space) for any integer $N$ prime to $D$. This generalizes the results of Krieg from $N = 1$ to arbitrary level. Combining this isomorphism with the recent work of Berger and Klosin and a modification of Ikeda's construction we prove the existence of a lift from the space of elliptic modular forms to the space of hermitian modular forms of level $N$ which can be viewed as a generalization of the classical hermitian Maass lift to arbitrary level.
","abstract_html":"<p>For an imaginary quadratic field $K$ of discriminant $-D$, let \\chi = \\chiK be the associated quadratic character. We will show that the space of special hermitian Jacobi forms of level $N$ is isomorphic to the space of plus forms of level $DN$ and nebentypus $\\chi$ (the hermitian analogue of Kohnen's plus space) for any integer $N$ prime to $D$. This generalizes the results of Krieg from $N = 1$ to arbitrary level. Combining this isomorphism with the recent work of Berger and Klosin and a modification of Ikeda's construction we prove the existence of a lift from the space of elliptic modular forms to the space of hermitian modular forms of level $N$ which can be viewed as a generalization of the classical hermitian Maass lift to arbitrary level.</p>","abstract_has_math":true,"creators":["Vu, An Hoa"],"institution":"The Graduate School and University Center of The City University of New York","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Krzysztof Klosin"],"committee_chairs":[],"committee_members":["Kenneth Kramer","Brooke Feigon"],"year":2019,"date_issued":"2019-09-01T07:00:00Z","date_published":"2019-09-01T07:00:00Z","updated_at":"2026-07-24T01:58:49Z","subjects":["Number Theory","modular forms","Hermitian modular forms","Maass lift","Saito-Kurokawa lift"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://academicworks.cuny.edu/gc_etds/3355","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Krzysztof Klosin"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Kenneth Kramer","Brooke Feigon"]},{"key":"dc:creator","label":"Author","values":["Vu, An Hoa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2021-09-30T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Graduate School and University Center of The City University of New York"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Number Theory","modular forms","Hermitian modular forms","Maass lift","Saito-Kurokawa lift"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://academicworks.cuny.edu/gc_etds/3355"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["For an imaginary quadratic field $K$ of discriminant $-D$, let $\\chi = \\chi_K$ be the associated quadratic character. We will show that the space of special hermitian Jacobi forms of level $N$ is isomorphic to the space of plus forms of level $DN$ and nebentypus $\\chi$ (the hermitian analogue of Kohnen's plus space) for any integer $N$ prime to $D$. This generalizes the results of Krieg from $N = 1$ to arbitrary level. Combining this isomorphism with the recent work of Berger and Klosin and a modification of Ikeda's construction we prove the existence of a lift from the space of elliptic modular forms to the space of hermitian modular forms of level $N$ which can be viewed as a generalization of the classical hermitian Maass lift to arbitrary level.
"]},{"key":"dc:title","label":"Title","values":["Hermitian Maass Lift for General Level"]}]}],"canonical_facts":{"dc:contributor.advisor":["Krzysztof Klosin"],"dc:contributor.committeemember":["Kenneth Kramer","Brooke Feigon"],"dc:creator":["Vu, An Hoa"],"dc:date.available":["2021-09-30T07:00:00Z"],"dc:description.abstract":["For an imaginary quadratic field $K$ of discriminant $-D$, let $\\chi = \\chi_K$ be the associated quadratic character. We will show that the space of special hermitian Jacobi forms of level $N$ is isomorphic to the space of plus forms of level $DN$ and nebentypus $\\chi$ (the hermitian analogue of Kohnen's plus space) for any integer $N$ prime to $D$. This generalizes the results of Krieg from $N = 1$ to arbitrary level. Combining this isomorphism with the recent work of Berger and Klosin and a modification of Ikeda's construction we prove the existence of a lift from the space of elliptic modular forms to the space of hermitian modular forms of level $N$ which can be viewed as a generalization of the classical hermitian Maass lift to arbitrary level.
"],"dc:identifier":["https://academicworks.cuny.edu/gc_etds/3355"],"dc:subject":["Number Theory","modular forms","Hermitian modular forms","Maass lift","Saito-Kurokawa lift"],"dc:title":["Hermitian Maass Lift for General Level"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Graduate School and University Center of The City University of New York"]},"updated_at":"2026-07-24T01:58:49Z"}