Dirichlet Series Explorer
Visualize how L-functions and their partial sums behave in the complex plane
Function
Choose L-function:
ζ(s) — Riemann Zeta
η(s) — Dirichlet Eta
L(s,χ₄) — χ mod 4
L(s,χ₃) — χ mod 3
Terms N:
40
Im(s) range:
30
Animation speed:
1
Heatmap |f|
Phase arg(f)
Re(f)
Spiral path
ζ(s) = Σ n⁻ˢ (n=1..N)
= Π (1-p⁻ˢ)⁻¹ (Euler)
The
Euler product
connects primes to the zeta function.
In
spiral view
, each prime factor spirals the partial product in the complex plane — watch convergence or divergence.
Zeros visible as dark spots in heatmap. Critical line at Re(s)=½ shown dashed.