Mean square of inverses of Dirichlet $L$-functions involving conductors

Iu-Iong Ng; Yuichiro Toma

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arXiv · 2501.11316

Mean square of inverses of Dirichlet $L$-functions involving conductors

Iu-Iong Ng·Yuichiro Toma

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Abstract

We deal with negative square moments of Dirichlet $L$-functions. Summing over characters modulo $q$, we obtain an asymptotic formula for the negative second moment of $L(1,χ)$ involving conductors. As an application, we give the improved lower bound on the success probability of the algorithm which recovers a short generator of the input generator of a principal ideal sampled from a specific Gaussian distribution in cyclotomic number fields.

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Iu-Iong Ng, Yuichiro Toma. 2025-01-20. Mean square of inverses of Dirichlet $L$-functions involving conductors. https://arxiv.org/abs/2501.11316

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