Mean square of inverses of Dirichlet $L$-functions involving conductors
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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
advanced mathematical theories
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Journal of the Mathematical Society of Japan
- Volume
- -1
- Issue
- -1
- Publication date
- 19 June 2026
- Language
- EN