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arXiv · 2609.01101

Sharp lower bounds for shifted moments of Dedekind zeta functions

Benjamin Durkan·Nilmoni Karak·Kamalakshya Mahatab
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Abstract

Let $K_1,\cdots,K_r$ be fixed number fields, and let $L$ be the compositum of their Galois closures. Assuming GRH for $\zeta_L$, 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 $\textrm{Gal}(L/\mathbb{Q})$. 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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Benjamin Durkan, Nilmoni Karak, Kamalakshya Mahatab. 2026-09-01. Sharp lower bounds for shifted moments of Dedekind zeta functions. https://arxiv.org/abs/2609.01101

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