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dc.contributor.authorAhlquist, Victor
dc.date.accessioned2023-02-13T14:18:03Z
dc.date.available2023-02-13T14:18:03Z
dc.date.issued2023-02-13
dc.identifier.urihttps://hdl.handle.net/2077/74926
dc.description.abstractWe 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.en
dc.language.isoengen
dc.subjectMathematics, number theory, cubic fields, L-functions, low-lying zeros, onelevel density, two-level density, phase transition.en
dc.titleThe low-lying zeros of L-functions associated to non-Galois cubic fieldsen
dc.typetext
dc.setspec.uppsokPhysicsChemistryMaths
dc.type.uppsokH2
dc.contributor.departmentUniversity of Gothenburg/Department of Mathematical Scienceeng
dc.contributor.departmentGöteborgs universitet/Institutionen för matematiska vetenskaperswe
dc.type.degreeStudent essay


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