Low-lying zeros of quadratic Dirichlet L-functions, hyper-elliptic curves and random matrix theory
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 …
and Sarnak to be given by the scaling limit of eigenvalues from the unitary symplectic …
Symplectic -level densities with restricted support
AM Mason, NC Snaith - Random Matrices: Theory and Applications, 2016 - World Scientific
In this paper, we demonstrate that the alternative form, derived by us in an earlier paper, of
the n-level densities for eigenvalues of matrices from the classical compact group US p (2 N) …
the n-level densities for eigenvalues of matrices from the classical compact group US p (2 N) …
Moments of traces of random symplectic matrices and hyperelliptic -functions
A Entin, N Pirani - arXiv preprint arXiv:2409.04844, 2024 - arxiv.org
We study matrix integrals of the form $$\int_ {\mathrm {USp (2n)}}\prod_ {j= 1}^ k\mathrm
{tr}(U^ j)^{a_j}\mathrm d U, $$ where $ a_1,\ldots, a_r $ are natural numbers and integration …
{tr}(U^ j)^{a_j}\mathrm d U, $$ where $ a_1,\ldots, a_r $ are natural numbers and integration …
[PDF][PDF] ON THE MOMENTS OF ONE-LEVEL DENSITIES IN FAMILIES OF HOLOMORPHIC CUSP FORMS IN THE LEVEL ASPECT
P COHEN, J DELL, OE GONZÁLEZ, G IYER… - 2024 - sashashkov.github.io
We study the n th centered moments of the 1-level density for the low-lying zeros of L-
functions attached to holomorphic cuspidal newforms of large prime level and fixed weight …
functions attached to holomorphic cuspidal newforms of large prime level and fixed weight …
[PDF][PDF] CURVES AND ZETA FUNCTIONS OVER FINITE FIELDS ARIZONA WINTER SCHOOL 2014: ARITHMETIC STATISTICS
C DAVID - 2014 - swc-math.github.io
The lectures will be concerned with statistics for the zeroes of L-functions in natural families.
This will include discussions of the number field and the function field case (the latter case …
This will include discussions of the number field and the function field case (the latter case …
[PDF][PDF] 2014 ARIZONA WINTER SCHOOL: ARITHMETIC STATISTICS STATISTICS FOR ZEROES OF L-FUNCTIONS OF CURVES OVER FINITE FIELDS
C DAVID - swc.math.arizona.edu
The lectures will be concerned with statistics for the zeroes of L-functions in natural families.
This will include discussions of the number field and the function field case (the latter case …
This will include discussions of the number field and the function field case (the latter case …