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

TL;DR

This paper provides comprehensive tables of Dirichlet characters, L-series, and prime zeta functions for small moduli, enabling precise numerical analysis and reference for related number theory research.

Contribution

It offers detailed tabulations and high-precision computations of Dirichlet L-series and prime zeta functions for small moduli, filling a gap in accessible reference data.

Findings

Tabulated Dirichlet characters for moduli up to 195.

Computed L-series and derivatives with high precision.

Introduced prime zeta functions related to Dirichlet L-series.

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.