Improve C82 upper bound#87
Open
maaxgrin wants to merge 2 commits into
Open
Conversation
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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.
This PR improves the recorded upper bound for C82, the essential minimum of the Zhang--Zagier height, from
to the certified bound
The construction uses the polynomials P1,...,P9,Q1,Q2 introduced by C. Doche in Zhang-Zagier heights of perturbed polynomials, J. Theor. Nombres Bordeaux 13 (2001), no. 1, 103--110. Starting from Q1,Q2, the computation adds the perturbative factors
The final denominator is
For this Q, optimizing the perturbative numerator exponents gives the numerical value
0.253626920959; the interval-certified upper bound is0.2536331090204145.The code, tests, certification run, and finite-family search report are available here:
https://github.com/maaxgrin/zhang-zagier-c82-bound