Agenda Structural Challenge Canonical mathematics structural-challenge, mathematics The order of vanishing of the L-function of an elliptic curve at s=1 equals the rank of the Mordell–Weil group.
Mathematics Structural Challenge Ledger

Birch and Swinnerton-Dyer Conjecture

CB-BSD canonical benchmark canonical benchmarks External: externally open τ response: structurally constrained

The order of vanishing of the L-function of an elliptic curve at s=1 equals the rank of the Mordell–Weil group.

See the paired Birch and Swinnerton-Dyer Conjecture — Challenge Response on the Results lane for the program's current response status, registry evidence, verification route, and external-review boundary.

Current status: structurally constrained.

Challenge statement

The order of vanishing of the L-function of an elliptic curve at s=1 equals the rank of the Mordell–Weil group.

Why this challenge is in the ledger

Arithmetic-geometry-spectral conjecture sitting at the heart of the Langlands programme.

τ-facing burden

Clarify how τ-zeta or τ-L-functions interact with elliptic curve L-functions and rank conjectures.

Bibliography clusters whose prior art bears on this page. Each cluster links to its representative references and to the broader Deep Comparison briefing.

Source: prior-art cluster index · canonical data lives in corpus/data/bibliography/prior-art-clusters.yml

First reviewer questions

  1. Can τ express elliptic curve rank?
  2. Does τ connect to the classical L-function?
  3. Are there τ-native rank predictions?

Source anchors

Source anchors are background references, not endorsements of Panta Rhei claims.

Save or share this page for inspection

Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.

Email to expert