The sixth power moment of Dirichlet L-functions

JB Conrey; H Iwaniec; K Soundararajan

doi:10.1007/s00039-012-0191-6

The sixth power moment of Dirichlet L-functions

JB Conrey, H Iwaniec, K Soundararajan

Research output: Contribution to journal › Article (Academic Journal) › peer-review

17 Citations (Scopus)

Abstract

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.

Translated title of the contribution	The sixth moment of Dirichlet L-functions
Original language	English
Pages (from-to)	1257-1288
Number of pages	32
Journal	Geometric and Functional Analysis
Volume	22
Issue number	5
DOIs	https://doi.org/10.1007/s00039-012-0191-6
Publication status	Published - Oct 2012

Access to Document

10.1007/s00039-012-0191-6

http://link.springer.com/article/10.1007/s00039-012-0191-6

Handle.net

Persistent link

Cite this

@article{6f2918112fc64419b8ffca4f4cbbb298,

title = "The sixth power moment of Dirichlet L-functions",

abstract = "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.",

author = "JB Conrey and H Iwaniec and K Soundararajan",

year = "2012",

month = oct,

doi = "10.1007/s00039-012-0191-6",

language = "English",

volume = "22",

pages = "1257--1288",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "5",

}

TY - JOUR

T1 - The sixth power moment of Dirichlet L-functions

AU - Conrey, JB

AU - Iwaniec, H

AU - Soundararajan, K

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.

U2 - 10.1007/s00039-012-0191-6

DO - 10.1007/s00039-012-0191-6

M3 - Article (Academic Journal)

SN - 1016-443X

VL - 22

SP - 1257

EP - 1288

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 5

ER -

The sixth power moment of Dirichlet L-functions

Abstract

Access to Document

Handle.net

Fingerprint

Cite this