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Lower Bounds for Localised Moments of Automorphic L-functions
Abstract
In this article, we describe a method to obtain lower bounds for the 2k-th moment of values of L-functions localised at the central point for all real k > 0. In particular, for the families of quadratic twists of self-dual irreducible unitary cuspidal automorphic representations of GLD(𝔸ℚ) with D∈{2,3,4}, our results are new in the range 0<k<1/2 when D∈{2,3}, and new for all k>0 when D=4.
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BibTeX
@misc{thakur2026lower,
title = {{Lower Bounds for Localised Moments of Automorphic $L$-functions}},
author = {Deep Thakur},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.32673},
eprint = {2609.32673},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32673},
}
RIS
TY - UNPB
TI - Lower Bounds for Localised Moments of Automorphic L-functions
AU - Deep Thakur
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2609.32673
UR - https://arxiv.org/abs/2609.32673
AB - In this article, we describe a method to obtain lower bounds for the 2k-th moment of values of L-functions localised at the central point for all real k > 0. In particular, for the families of quadratic twists of self-dual irreducible unitary cuspidal automorphic representations of GL_D(𝔸_ℚ) with D∈{2,3,4}, our results are new in the range 0<k<1/2 when D∈{2,3}, and new for all k>0 when D=4.
ER -