PreprintCC BY 4.0arXiv
A secondary term in the first moment of primitive cubic Dirichlet L-functions
Abstract
P. Gao and L. Zhao obtained an asymptotic formula for the smoothed first moment of primitive cubic Dirichlet L-functions over Q with conductors coprime to $3$, with a main term of order Q and error O(Q7/8+eps) under the generalized Lindelöf hypothesis. Building on their double Dirichlet series, we assume the generalized Riemann hypothesis and separate an explicit secondary term of order Q5/6, with error O(Q23/28+eps).
Related
- The First Moment of Dirichlet L-functions over Generators of the Character Group
- Improved first moments of primitive quartic and sextic Dirichlet L-functions
- The first moment of quadratic Dirichlet L-functions in the even hyperelliptic ensemble
- A secondary term in the first moment of cubic L-functions over function fields
- Upper Bounds on the de Bruijn-Newman constant for Dirichlet L-functions with primitive real-valued characters
BibTeX
@misc{hong2026secondary,
title = {{A secondary term in the first moment of primitive cubic Dirichlet L-functions}},
author = {Ziwei Hong},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01451},
eprint = {2611.01451},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01451},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A secondary term in the first moment of primitive cubic Dirichlet L-functions
AU - Ziwei Hong
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01451
UR - https://arxiv.org/abs/2611.01451
AB - P. Gao and L. Zhao obtained an asymptotic formula for the smoothed first moment of primitive cubic Dirichlet L-functions over Q with conductors coprime to $3$, with a main term of order Q and error O(Q^7/8+eps) under the generalized Lindelöf hypothesis. Building on their double Dirichlet series, we assume the generalized Riemann hypothesis and separate an explicit secondary term of order Q^5/6, with error O(Q^23/28+eps).
ER -