Dirichlet L-functions

Plots L-functions for Dirichlet characters.

A small MATLAB toolbox to validate Dirichlet characters and numerically evaluate/plot the

Dirichlet L-function L(s,χ). Includes a ζ(s) demo and produces nice complex-plane heatmaps of

log10|L(s,χ)| plus critical-line plots.

Input format:

- Provide a Dirichlet character modulo N as a length-N complex vector chiIn.

- Default convention: chiIn(k+1) = χ(k mod N) for k = 0,...,N−1.

Example (quadratic character mod 5): χ = [0, 1, -1, -1, 1].

Validation:

- checks χ(n)=0 if gcd(n,N)≠1, |χ(n)|≈1 on units, and multiplicativity on (Z/NZ)^×.

Outputs:

- evaluation of L(s,χ), and plots over a chosen complex rectangle.