feat: formalize Green's Open Problem 82 - #5067
Open
alexgrebeshok-coder wants to merge 1 commit into
Open
Conversation
Statement of Ben Green's open problem 82 (Littlewood's cosine zeros) plus the known bounds from the comments, as sorry-theorems. Fixes google-deepmind#1737
github-actions
Bot
added
the
green-problems
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Summary
Formalises Ben Green's open problem 82 (how many zeros a cosine polynomial on ℝ/ℤ must have) and the known bounds from the comments (Borwein–Erdélyi–Ferguson–Lockhart, Juškevičius–Sahasrabudhe, Sahasrabudhe, Bedert).
Convention:
cos(aθ)on ℝ/ℤ is(fourier a θ).re, i.e.cos(2π a θ). The open item isminNumCosineZeros, not the disproved guessn-1.Check
lake --wfail build 'FormalConjectures.GreensOpenProblems.«82»'FormalConjectures/GreensOpenProblems/82.leanFixes #1737