theta

Research and experiments around theta functions, elliptic functions, and possible mathematical toys/games built from them.

Research notes

The first research pass follows two routes:

• Richard E. Borcherds's short elliptic-functions lecture series, plus his theta-function lectures in the modular-forms series.
• David Mumford's Tata Lectures on Theta I–III.

Start here:

• research/borcherds-lectures.md — summaries of the four elliptic-function lectures plus the two modular-forms theta lectures.
• research/mumford-tata-lectures.md — section-by-section map of all three Tata Lectures volumes and the reason for their development order.
• research/source-index.md — verified lecture links, explicit bibliography, access/copyright notes, and background-source separation.
• sources/jahnke-emde.md — the old function-table book explicitly cited by Borcherds, including exact printed pages and Archive leaf numbers for the theta/Jacobi/Weierstrass/sigma material.
• sources/fetch-jahnke-emde.sh — reproducible fetch of the Internet Archive/Digital Library of India PDF whose item metadata marks it public domain.

Source material is kept conceptually separate from our summaries. Public-domain material gets a reproducible fetch path; copyrighted-but-author-hosted books are linked rather than copied into the repository.