PreprintCC BY 4.0arXiv
Sharp lower bounds for shifted moments of Dedekind zeta functions
Abstract
Let K1,⋯,Kr be fixed number fields, and let L be the compositum of their Galois closures. Assuming GRH for ζL, we prove a sharp lower bound for products of shifted Dedekind zeta functions on the critical line, for arbitrary fixed positive real exponents and uniformly for shifts of size at most T/2. The correlation factor is expressed as a product of Dedekind zeta functions of the fixed fields of double-coset stabilisers in Gal(L/ℚ). Combined with the corresponding upper bound by the authors, determines the order of magnitude of these shifted moments for both Galois and non-Galois fields.
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BibTeX
@misc{durkan2026sharp,
title = {{Sharp lower bounds for shifted moments of Dedekind zeta functions}},
author = {Benjamin Durkan and Nilmoni Karak and Kamalakshya Mahatab},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01101},
eprint = {2609.01101},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01101},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp lower bounds for shifted moments of Dedekind zeta functions
AU - Benjamin Durkan
AU - Nilmoni Karak
AU - Kamalakshya Mahatab
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01101
UR - https://arxiv.org/abs/2609.01101
AB - Let K_1,⋯,K_r be fixed number fields, and let L be the compositum of their Galois closures. Assuming GRH for ζ_L, we prove a sharp lower bound for products of shifted Dedekind zeta functions on the critical line, for arbitrary fixed positive real exponents and uniformly for shifts of size at most T/2. The correlation factor is expressed as a product of Dedekind zeta functions of the fixed fields of double-coset stabilisers in Gal(L/ℚ). Combined with the corresponding upper bound by the authors, determines the order of magnitude of these shifted moments for both Galois and non-Galois fields.
ER -