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Distribution of central values of Hecke L-functions of n-th order characters
Abstract
We prove a one-sided central limit theorem for log |L(1/2,χ)| in a thin family of n-th order Hecke characters, for n ≥ 3. The proof combines the method of Radziwiłł and Soundararajan with a recent asymptotic formula of Diaconu, Ion, Paşol, and Popa for the twisted second moment with a power-saving error term. We also obtain upper bounds of the conjectured order of magnitude for the 2k-th moments for 0< k< 1.
Related
- Non-vanishing of central values of angular Hecke L-functions
- Large values of quadratic Hecke L-functions with prime-related moduli of the Gaussian field
- Irrationality of values of L-functions for real Dirichlet characters
- Finite Cotangent Power Sums Weighted by Additive Characters With Application to Mean Values of Additive-and-Multiplicatively Twisted L-Functions
- Extreme values of quadratic Hecke L-functions
BibTeX
@misc{mcgoldrick2026distribution,
title = {{Distribution of central values of Hecke $L$-functions of $n$-th order characters}},
author = {Lewis McGoldrick},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17144},
eprint = {2610.17144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17144},
}
RIS
TY - UNPB
TI - Distribution of central values of Hecke L-functions of n-th order characters
AU - Lewis McGoldrick
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17144
UR - https://arxiv.org/abs/2610.17144
AB - We prove a one-sided central limit theorem for log |L(1/2,χ)| in a thin family of n-th order Hecke characters, for n ≥ 3. The proof combines the method of Radziwiłł and Soundararajan with a recent asymptotic formula of Diaconu, Ion, Paşol, and Popa for the twisted second moment with a power-saving error term. We also obtain upper bounds of the conjectured order of magnitude for the 2k-th moments for 0< k< 1.
ER -