Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300605588> ?p ?o ?g. }
Showing items 1 to 93 of
93
with 100 items per page.
- W4300605588 abstract "The statistics of low-lying zeros of quadratic Dirichlet L-functions were conjectured by Katz and Sarnak to be given by the scaling limit of eigenvalues from the unitary symplectic ensemble. The n-level densities were found to be in agreement with this in a certain neighborhood of the origin in the Fourier domain by Rubinstein in his Ph.D. thesis in 1998. An attempt to extend the neighborhood was made in the Ph.D. thesis of Peng Gao (2005), who under GRH gave the density as a complicated combinatorial factor, but it remained open whether it coincides with the Random Matrix Theory factor. For n at most 7 this was recently confirmed by Levinson and Miller. We resolve this problem for all n, not by directly doing the combinatorics, but by passing to a function field analogue, of L-functions associated to hyper-elliptic curves of given genus g over a field of q elements. We show that the answer in this case coincides with Gao's combinatorial factor up to a controlled error. We then take the limit of large finite field size q to infinity and use the Katz-Sarnak equidistribution theorem, which identifies the monodromy of the Frobenius conjugacy classes for the hyperelliptic ensemble with the group USp(2g). Further taking the limit of large genus g to infinity allows us to identify Gao's combinatorial factor with the RMT answer." @default.
- W4300605588 created "2022-10-03" @default.
- W4300605588 creator A5038687995 @default.
- W4300605588 creator A5050491209 @default.
- W4300605588 creator A5079706565 @default.
- W4300605588 date "2012-08-29" @default.
- W4300605588 modified "2023-10-16" @default.
- W4300605588 title "Low-lying zeros of quadratic Dirichlet L-functions, hyper-elliptic curves and Random Matrix Theory" @default.
- W4300605588 doi "https://doi.org/10.48550/arxiv.1208.5962" @default.
- W4300605588 hasPublicationYear "2012" @default.
- W4300605588 type Work @default.
- W4300605588 citedByCount "0" @default.
- W4300605588 crossrefType "posted-content" @default.
- W4300605588 hasAuthorship W4300605588A5038687995 @default.
- W4300605588 hasAuthorship W4300605588A5050491209 @default.
- W4300605588 hasAuthorship W4300605588A5079706565 @default.
- W4300605588 hasBestOaLocation W43006055881 @default.
- W4300605588 hasConcept C105795698 @default.
- W4300605588 hasConcept C106487976 @default.
- W4300605588 hasConcept C114614502 @default.
- W4300605588 hasConcept C121332964 @default.
- W4300605588 hasConcept C122123141 @default.
- W4300605588 hasConcept C134306372 @default.
- W4300605588 hasConcept C138405894 @default.
- W4300605588 hasConcept C151201525 @default.
- W4300605588 hasConcept C157369684 @default.
- W4300605588 hasConcept C158693339 @default.
- W4300605588 hasConcept C159985019 @default.
- W4300605588 hasConcept C168619227 @default.
- W4300605588 hasConcept C169214877 @default.
- W4300605588 hasConcept C179603306 @default.
- W4300605588 hasConcept C182310444 @default.
- W4300605588 hasConcept C182514268 @default.
- W4300605588 hasConcept C192562407 @default.
- W4300605588 hasConcept C202444582 @default.
- W4300605588 hasConcept C24084028 @default.
- W4300605588 hasConcept C2524010 @default.
- W4300605588 hasConcept C33923547 @default.
- W4300605588 hasConcept C59822182 @default.
- W4300605588 hasConcept C62520636 @default.
- W4300605588 hasConcept C64812099 @default.
- W4300605588 hasConcept C77926391 @default.
- W4300605588 hasConcept C86803240 @default.
- W4300605588 hasConcept C87945829 @default.
- W4300605588 hasConcept C95707001 @default.
- W4300605588 hasConcept C96403706 @default.
- W4300605588 hasConcept C99844830 @default.
- W4300605588 hasConceptScore W4300605588C105795698 @default.
- W4300605588 hasConceptScore W4300605588C106487976 @default.
- W4300605588 hasConceptScore W4300605588C114614502 @default.
- W4300605588 hasConceptScore W4300605588C121332964 @default.
- W4300605588 hasConceptScore W4300605588C122123141 @default.
- W4300605588 hasConceptScore W4300605588C134306372 @default.
- W4300605588 hasConceptScore W4300605588C138405894 @default.
- W4300605588 hasConceptScore W4300605588C151201525 @default.
- W4300605588 hasConceptScore W4300605588C157369684 @default.
- W4300605588 hasConceptScore W4300605588C158693339 @default.
- W4300605588 hasConceptScore W4300605588C159985019 @default.
- W4300605588 hasConceptScore W4300605588C168619227 @default.
- W4300605588 hasConceptScore W4300605588C169214877 @default.
- W4300605588 hasConceptScore W4300605588C179603306 @default.
- W4300605588 hasConceptScore W4300605588C182310444 @default.
- W4300605588 hasConceptScore W4300605588C182514268 @default.
- W4300605588 hasConceptScore W4300605588C192562407 @default.
- W4300605588 hasConceptScore W4300605588C202444582 @default.
- W4300605588 hasConceptScore W4300605588C24084028 @default.
- W4300605588 hasConceptScore W4300605588C2524010 @default.
- W4300605588 hasConceptScore W4300605588C33923547 @default.
- W4300605588 hasConceptScore W4300605588C59822182 @default.
- W4300605588 hasConceptScore W4300605588C62520636 @default.
- W4300605588 hasConceptScore W4300605588C64812099 @default.
- W4300605588 hasConceptScore W4300605588C77926391 @default.
- W4300605588 hasConceptScore W4300605588C86803240 @default.
- W4300605588 hasConceptScore W4300605588C87945829 @default.
- W4300605588 hasConceptScore W4300605588C95707001 @default.
- W4300605588 hasConceptScore W4300605588C96403706 @default.
- W4300605588 hasConceptScore W4300605588C99844830 @default.
- W4300605588 hasLocation W43006055881 @default.
- W4300605588 hasOpenAccess W4300605588 @default.
- W4300605588 hasPrimaryLocation W43006055881 @default.
- W4300605588 hasRelatedWork W1506078959 @default.
- W4300605588 hasRelatedWork W2001311207 @default.
- W4300605588 hasRelatedWork W2030926133 @default.
- W4300605588 hasRelatedWork W2097123157 @default.
- W4300605588 hasRelatedWork W2138191633 @default.
- W4300605588 hasRelatedWork W2148028512 @default.
- W4300605588 hasRelatedWork W2949296370 @default.
- W4300605588 hasRelatedWork W2951593550 @default.
- W4300605588 hasRelatedWork W3137286201 @default.
- W4300605588 hasRelatedWork W4286741676 @default.
- W4300605588 isParatext "false" @default.
- W4300605588 isRetracted "false" @default.
- W4300605588 workType "article" @default.