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… proof Following the Zulip discussion (Sphere packing in 8 dimensions > SphereCeti): - The bound |τ(p)| ≤ 2 p^(11/2) is Ramanujan's conjecture alone; the Ramanujan–Petersson conjecture is Petersson's generalisation to all cuspidal eigenforms. Retitle the problem and update the notes and Lean docstrings accordingly, and drop Petersson's paper from the sources. - The informal proof wrongly located τ(p) in the étale cohomology of the universal elliptic curve. Weight-12 eigenvalues live in H¹_! of the modular curve with coefficients in Sym¹⁰ R¹f_*Q_ℓ, and through it in H¹¹ of the 10-fold fibre power (Kuga–Sato variety). Rewrite the sketch: Eichler–Shimura isomorphism and congruence relation give X² − τ(p)X + p¹¹, and purity comes either from Weil I applied to a smooth compactification of the Kuga–Sato variety (Deligne 1969/1974) or from Weil II applied to the sheaf directly (Freitag–Kiehl). Add the Weil II and Freitag–Kiehl references. The problem ID and the theorem name stay `ramanujan_petersson`: the ID is a member of the frozen v1 set, and renaming the theorem would change the trusted statement and require a statement revision. The Lean statement itself is unchanged. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01SXjhFkcnZG1eciaA1Rjhdh
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@alreadydone Could you review this one? |
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Nov 7, 2026
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Nov 7, 2026
Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
alreadydone
reviewed
Nov 7, 2026
Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
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Following the Zulip discussion #Sphere packing in 8 dimensions > SphereCeti @ 💬
The conjecture for$\tau(p)$ is due to Ramanujan, where Ramanujan-Petersson refers to the general statement on cuspidal Hecke eigenforms. But it seems that the id is frozen so I only change the docstring. Also, informal proofs are corrected, following the above Zulip discussion.
This was (again) written by Claude, so it would be great if someone can take a look.