Zeros of L-functions and large partial sums of Dirichlet coefficients
Abstract
Abstract Let $$L(s,\pi )=\sum _{n=1}^{\infty }\lambda _{\pi }(n)n^{-s}$$ L ( s , π ) = ∑ n = 1 ∞ λ π ( n ) n - s be an L -function that satisfies a weak form of the generalized Ramanujan conjecture. We prove that large partial sums of $$\lambda _{\pi }(n)$$ λ π ( n ) strongly repel the low-lying zeros of $$L(s,\pi )$$ L ( s , π ) away from the critical line. Our results extend and quantitatively improve preceding work of Granville and Soundararajan.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Algebra and Geometry
Advanced Mathematical Identities
Publication details
- Journal / source
- Mathematische Annalen
- Publisher
- Springer Science and Business Media LLC
- Volume
- 396
- Issue
- 1
- Publication date
- 28 August 2026
- Language
- EN