Dirichlet L-functions: figures and editable sources

Course contents

Original programme diagrams, with their editable SVGs and reproducible Python sources. Finite computations and numerical samples are distinguished from the arguments in the lessons.

Beta explicit formula

The character-weighted prime-power step function and the explicit-formula approximation from ten zero pairs.

Lesson · PNG · Editable SVG · Python source

Character determinant fibre

An exact determinant fibre with five labelled lattice points and the three weighted-count terms at q equal to 5 to the fourth times 7 cubed.

Lesson · PNG · Editable SVG · Python source · Exact example data

Character partial sums

Exact partial sums of the Legendre characters at primes 7, 11 and 23, with integer endpoints, maxima and least nonresidues labelled.

Lesson · PNG · Editable SVG · Python source

Gauss sum paths

Ordered unit-vector sums for p equals 5 and 7, with each arrow labelled by n and endpoints at positive square root of 5 and positive i times square root of 7.

Lesson · PNG · Editable SVG · Python source

Orthogonality

Two complex-plane diagrams: all four characters modulo 5 have value 1 at n equals 1, while their values at n equals 2 are 1, i, minus 1 and minus i, which cancel.

Lesson · PNG · Editable SVG · Python source

Prime race modulo 4

The exact difference of the prime counts in the residue classes 3 and 1 modulo 4 up to one hundred thousand, plotted against logarithmic x.

Lesson · PNG · Editable SVG · Python source

The mathematical diagrams are CC0 1.0. DejaVu font terms remain applicable to glyphs. Machine-readable figure catalogue.