dc.contributor.advisor | Pitale, Ameya | |
dc.contributor.author | Dynes, Patrick | |
dc.date.accessioned | 2023-04-25T18:52:42Z | |
dc.date.available | 2023-04-25T18:52:42Z | |
dc.date.issued | 2023-05-12 | |
dc.identifier.uri | https://hdl.handle.net/11244/337463 | |
dc.description.abstract | This thesis is motivated by the problem of studying the Ikeda lift via a converse theorem due
to R. Weissauer. We investigate a certain function; denoted by 𝜙(𝑎; 𝐵), where 𝑎 is a positive
integer and 𝐵 is a symmetric positive-definite half-integral matrix; appearing in the Fourier
coefficient formulas of a linear version of the Ikeda lift due to W. Kohnen. We develop
new methods for computing 𝜙(𝑎; 𝐵) via the extended Gross-Keating (EGK) datum of a
quadratic form and develop novel combinatorial interpretations for 𝜙(𝑎; 𝐵) which involve
integer partitions with restrictions depending on the EGK datum attached to 𝐵 at each prime. | en_US |
dc.language | en | en_US |
dc.rights | Attribution-NonCommercial-ShareAlike 4.0 International | * |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-sa/4.0/ | * |
dc.subject | Mathematics, Number Theory, Automorphic Forms | en_US |
dc.title | Combinatorial Aspects of the Ikeda Lift via Extended Gross-Keating Data | en_US |
dc.contributor.committeeMember | Jablonski, Michael | |
dc.contributor.committeeMember | Martin, Kimball | |
dc.contributor.committeeMember | Muller, Greg | |
dc.contributor.committeeMember | Parthasarathy, Ramkumar | |
dc.contributor.committeeMember | Przebinda, Tomasz | |
dc.date.manuscript | 2023-04-23 | |
dc.thesis.degree | Ph.D. | en_US |
ou.group | Dodge Family College of Arts and Sciences::Department of Mathematics | en_US |
shareok.orcid | 0000-0002-3201-4162 | en_US |