The low-lying zeros of L-functions associated to non-Galois cubic fields
| dc.contributor.author | Ahlquist, Victor | |
| dc.contributor.department | Chalmers tekniska högskola / Institutionen för matematiska vetenskaper | sv |
| dc.contributor.examiner | Brandes, Julia | |
| dc.contributor.supervisor | Södergren, Anders | |
| dc.date.accessioned | 2023-03-14T14:35:40Z | |
| dc.date.available | 2023-03-14T14:35:40Z | |
| dc.date.issued | 2023 | |
| dc.date.submitted | 2023 | |
| dc.description.abstract | We study the low-lying zeros of Artin L-functions associated to non-Galois cubic number fields through their one- and two-level densities. In particular, we find new precise estimates for the two-level density with a power-saving error term. We apply the L-functions Ratios Conjecture to study these densities for a larger class of test functions than unconditional computations allow. By reviewing a known Ratios Conjecture prediction, due to Cho, Fiorilli, Lee, and Södergren, for the one-level density, we isolate a phase transition in the lower-order terms, which reveals a striking symmetry. Our computations show that the same symmetry exists in the one-level density of several other families, that have previously been studied in the literature, and this motivates us to formulate a conjecture extending one part of the Katz–Sarnak prediction for families of symplectic symmetry type. Moreover, we isolate several phase transitions in the lower-order terms of the two-level density. To the best of our knowledge, this is the first time such phase transitions have been observed in any n-level density with n ≥ 2. | |
| dc.identifier.uri | http://hdl.handle.net/20.500.12380/306006 | |
| dc.setspec.uppsok | PhysicsChemistryMaths | |
| dc.subject | Mathematics, number theory, cubic fields, L-functions, low-lying zeros, onelevel density, two-level density, phase transition | |
| dc.title | The low-lying zeros of L-functions associated to non-Galois cubic fields | |
| dc.type.degree | Examensarbete för masterexamen | sv |
| dc.type.degree | Master's Thesis | en |
| dc.type.uppsok | H | |
| local.programme | Övrigt, MSc |