Distribution of values of higher derivatives of $L'(s,χ)/L(s,χ)$
Abstract
In this article, we study the value distribution theory for the first derivative of the logarithmic derivative of Dirichlet $L$-functions, generalizing certain results of Ihara, Matsumoto et al. related to ``$M$-functions'' for $σ= \operatorname{Re}(s) > 1$. We then discuss the main obstruction toward generalization to higher derivatives.
Fields of Study & Subjects
Meromorphic and Entire Functions
Analytic Number Theory Research
Advanced Mathematical Identities
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 January 2026
- Document type
- Preprint