Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli

2010/08/15 by Richard J. Mathar, Mathar, Richard J.
Mathematics · #11M06 #11R42 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M06 #msc:11R42

paper · pdf · doi:10.48550/arxiv.1008.2547

Table extended to cover moduli <= 195 in the ancillary directory

openalex publication_date 2010/08/15 · arxiv created 2015/07/31 · arxiv updated 2015/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Dirichlet characters of reduced residue systems modulo m are tabulated for moduli m <= 195. The associated L-series are tabulated for m <= 14 and small positive integer argument s accurate to 10^(-50), their first derivatives for m <= 6. Restricted summation over primes only defines Dirichlet Prime L-functions which lead to Euler products (Prime Zeta Modulo functions). Both are materialized over similar ranges of moduli and arguments. Formulas and numerical techniques are well known; the aim is to provide direct access to reference values.

Related

• L-series associated to symmetric functions mod N with applications related to ζ(3), ζ(5)
• Formalizing zeta and L-functions in Lean
• On Littlewood's estimate for the modulus of the zeta function on the critical line
• A simple reformulation of Riemann Zeta function
• Survey of Dirichlet Series of Multiplicative Arithmetic Functions