An Arithmetic Sum Associated with the Classical Theta Function

formal-conjectures · arxiv · ams-11

**Conjecture 1.1**: For any odd prime $k$, the sum associated with the classical theta function $θ_3$,
$S(k)$ is positive.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/2501.03234
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Arxiv/2501.03234/ArithmeticSumS.lean
Local target: Corpus.Arxiv250103234ArithmeticSumS.conjecture_1_1
Source SHA-256: 4ccb27f627ba92aabf704cda1615528586500e5b9d0c8b0f8ada575c809600f6
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record