On Signs of Hecke eigenvalues of Siegel modular forms
| dc.contributor.advisor | Pitale, Ameya | |
| dc.contributor.author | Addanki, Nagarjuna Chary | |
| dc.contributor.committeeMember | Roche, Alan | |
| dc.contributor.committeeMember | Martin, Kimball | |
| dc.contributor.committeeMember | Garg, Jivtesh | |
| dc.date.accessioned | 2025-07-31T16:07:31Z | |
| dc.date.embargoExpiration | ||
| dc.date.issued | 2025 | |
| dc.date.proquestAvailable | 01/01/2025 | |
| dc.date.updated | 2025-07-31T16:07:31Z | |
| dc.description.abstract | Let <i>F</i> ∈ <i>S<sub>k+n</sub></i>(Γ<sub>2n</sub>) be an Ikeda lift and λ<i><sub>F</sub></i>(<i>m</i>) be the eigenvalue corresponding to Hecke operator <i>T(m)</i>. For a fixed <i>n</i> and <i>k</i>, we show that λ<i><sub>F</sub>(p)</i> is positive for all large enough primes <i>p</i>. For <i>n</i>=2, we show that, given <i>r</i> there exists <i>C<sub>r</sub></i> such that λ<i><sub>F</sub>(p<super>r</super>)</i> > 0 for all <i>p</i> > <i>C<sub>r</sub></i>. Let <i>F</i> ∈ <i>S<sub>k</sub></i><sub>1</sub>(Γ(2)(<i>N</i><sub>1</sub>)) and <i>G</i> ∈ <i>Sk</i>2 (Γ(2)(<i>N</i>2)) be two eigenforms that satisfy the Generalized Ramanujan Conjecture. We compute a lower bound for the density of the set of primes, {<i>p</i> : λ<i>F(p)</i>λ<i>G(p)</i> < 0}. | |
| dc.identifier.uri | https://shareok.org//handle/11244/341585 | |
| dc.language.iso | en | |
| dc.publisher | University of Oklahoma – Graduate College | |
| dc.subject | Mathematics | |
| dc.subject | Hecke eigenvalues | |
| dc.subject | Number Theory | |
| dc.subject | Siegel Modular forms | |
| dc.subject | Sign changes | |
| dc.thesis.degree | D.Phil. | |
| dc.title | On Signs of Hecke eigenvalues of Siegel modular forms | |
| ou.group | Mathematics: Arts & Sciences |