TY - JOUR
T1 - The Sixth Power Moment of Dirichlet L-Functions
AU - Conrey, J. B.
AU - Iwaniec, H.
AU - Soundararajan, K.
N1 - Funding Information:
Research supported in part by the American Institute of Mathematics and by the NSF grants DMS-1101774, DMS-1101575, and DMS 1001068.
PY - 2012/10
Y1 - 2012/10
N2 - We prove a formula, with power savings, for the sixth moment of Dirichlet L- functions averaged over all primitive characters χ (mod q) with q ≤ Q, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.
AB - We prove a formula, with power savings, for the sixth moment of Dirichlet L- functions averaged over all primitive characters χ (mod q) with q ≤ Q, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.
UR - http://www.scopus.com/inward/record.url?scp=84868149127&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84868149127&partnerID=8YFLogxK
U2 - 10.1007/s00039-012-0191-6
DO - 10.1007/s00039-012-0191-6
M3 - Article
AN - SCOPUS:84868149127
SN - 1016-443X
VL - 22
SP - 1257
EP - 1288
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 5
ER -