TY - JOUR
T1 - Artin-Schreier L-functions and random unitary matrices
AU - Entin, Alexei
N1 - Funding Information:
The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme ( FP7/2007-2013 )/ ERC grant agreement no. 320755 .
PY - 2014/12
Y1 - 2014/12
N2 - We give a new derivation of an identity due to Z. Rudnick and P. Sarnak about the n-level correlations of eigenvalues of random unitary matrices as well as a new proof of a formula due to M. Diaconis and P. Shahshahani expressing averages of trace products over the unitary matrix ensemble. Our method uses the zero statistics of Artin-Schreier L-functions and a deep equidistribution result due to N. Katz.
AB - We give a new derivation of an identity due to Z. Rudnick and P. Sarnak about the n-level correlations of eigenvalues of random unitary matrices as well as a new proof of a formula due to M. Diaconis and P. Shahshahani expressing averages of trace products over the unitary matrix ensemble. Our method uses the zero statistics of Artin-Schreier L-functions and a deep equidistribution result due to N. Katz.
KW - L-functions
KW - Random matrix theory
UR - http://www.scopus.com/inward/record.url?scp=84907331583&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2014.06.019
DO - 10.1016/j.jnt.2014.06.019
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84907331583
SN - 0022-314X
VL - 145
SP - 340
EP - 351
JO - Journal of Number Theory
JF - Journal of Number Theory
ER -