Skip to content

[Merged by Bors] - feat: bounds for modular forms of non-positive weights#18192

Closed
CBirkbeck wants to merge 35 commits intomasterfrom
CB_modforms_maxmod
Closed

[Merged by Bors] - feat: bounds for modular forms of non-positive weights#18192
CBirkbeck wants to merge 35 commits intomasterfrom
CB_modforms_maxmod

Conversation

@CBirkbeck
Copy link
Copy Markdown
Collaborator

@CBirkbeck CBirkbeck commented Oct 24, 2024

We use the Maximum modulus principle to show that modular forms of non-positive weights are bounded by its value of some element of the upper half plane imaginary part at least 1/2.


@github-actions
Copy link
Copy Markdown

github-actions bot commented Oct 24, 2024

PR summary 7d5154c184

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.NumberTheory.ModularForms.LevelOne 1646

Declarations diff

+ SlashInvariantForm.exists_one_half_le_im_and_norm_le
+ SlashInvariantForm.wt_eq_zero_of_eq_const
+ coe
+ coe_apply_complex
+ denom_S
+ denom_one
+ det_coe
+ exists_one_half_le_im_smul
+ exists_one_half_le_im_smul_and_norm_denom_le
+ three_le_four_mul_im_sq_of_mem_fd
-++- im_smul_eq_div_normSq

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.


Decrease in tech debt: (relative, absolute) = (1.00, 0.00)
Current number Change Type
1552 -1 erw

Current commit 7d5154c184
Reference commit 66df24a8e2

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@CBirkbeck CBirkbeck marked this pull request as ready for review October 25, 2024 15:57
@CBirkbeck CBirkbeck removed the WIP Work in progress label Oct 25, 2024
@grunweg grunweg changed the title Bounds for modular forms of non-positive weights feat: bounds for modular forms of non-positive weights Oct 25, 2024
@grunweg grunweg added the t-analysis Analysis (normed *, calculus) label Oct 25, 2024
@loefflerd
Copy link
Copy Markdown
Contributor

Following some discussion with @CBirkbeck, I've pushed some changes to this branch which avoid making subgroups of SL2Z into subtypes, which gets rid of some unnecessary coercions and API lemmas.

@CBirkbeck
Copy link
Copy Markdown
Collaborator Author

No problem! By the way, I realised while fixing the conflicts that we have two distinct namespaces ModularGroup and UpperHalfPlane.ModularGroup. Is this deliberate or should they be unified? In any case denom_one as presently formulated shouldn't be in the ModularGroup namespace, since the 1 is getting elaborated as 1 : ↥GL(2, ℝ)⁺ rather than as 1 : SL(2, ℤ).

No that was a mistake. I've removed it now and move denom_one.

@CBirkbeck CBirkbeck removed the awaiting-author A reviewer has asked the author a question or requested changes. label Nov 19, 2024
@loefflerd
Copy link
Copy Markdown
Contributor

(I can push fixes with all these changes to your PR, just let me know if that's OK with you.)

@CBirkbeck
Copy link
Copy Markdown
Collaborator Author

(I can push fixes with all these changes to your PR, just let me know if that's OK with you.)

Oh I was just doing this now. Go ahead and I'll double check there is nothing missing.

@loefflerd
Copy link
Copy Markdown
Contributor

I have pushed fixes, I believe everything outside the new file LevelOne is now OK. I have not looked in detail at the new file, other than fixing knock-on effects of the changes I made elsewhere. Looking at it now.

Copy link
Copy Markdown
Collaborator Author

@CBirkbeck CBirkbeck left a comment

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

I think the results like modular_S_smul and those near it should maybe also move down

@loefflerd
Copy link
Copy Markdown
Contributor

I think the results like modular_S_smul and those near it should maybe also move down

That doesn't work because it's used in exists_SL2_smul_eq_of_apply_zero_one_ne_zero (which is definitely not a ModularGroup lemma).

Copy link
Copy Markdown
Contributor

@loefflerd loefflerd left a comment

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Here are some comments on LevelOne.lean.

CBirkbeck and others added 3 commits November 19, 2024 22:34
Co-authored-by: David Loeffler <d.loeffler.01@cantab.net>
Co-authored-by: David Loeffler <d.loeffler.01@cantab.net>
Copy link
Copy Markdown
Contributor

@loefflerd loefflerd left a comment

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

I think this is good now. I just spotted two tiny cosmetic fixes.

maintainer delegate

@github-actions
Copy link
Copy Markdown

🚀 Pull request has been placed on the maintainer queue by loefflerd.

@github-actions github-actions bot added the maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. label Nov 20, 2024
@riccardobrasca
Copy link
Copy Markdown
Member

Thanks!

bors d+

@mathlib-bors
Copy link
Copy Markdown
Contributor

mathlib-bors bot commented Nov 20, 2024

✌️ CBirkbeck can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@github-actions github-actions bot added the delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). label Nov 20, 2024
CBirkbeck and others added 2 commits November 20, 2024 10:41
Co-authored-by: David Loeffler <d.loeffler.01@cantab.net>
@CBirkbeck
Copy link
Copy Markdown
Collaborator Author

bors r+

mathlib-bors bot pushed a commit that referenced this pull request Nov 20, 2024
We use the Maximum modulus principle to show that modular forms of non-positive weights are bounded by its value of some element of the upper half plane imaginary part at least 1/2.




Co-authored-by: Chris Birkbeck <c.birkbeck@ucl.ac.uk>
Co-authored-by: David Loeffler <d.loeffler.01@cantab.net>
@mathlib-bors
Copy link
Copy Markdown
Contributor

mathlib-bors bot commented Nov 20, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat: bounds for modular forms of non-positive weights [Merged by Bors] - feat: bounds for modular forms of non-positive weights Nov 20, 2024
@mathlib-bors mathlib-bors bot closed this Nov 20, 2024
@mathlib-bors mathlib-bors bot deleted the CB_modforms_maxmod branch November 20, 2024 10:54
TobiasLeichtfried pushed a commit that referenced this pull request Nov 21, 2024
add two results:

-  If `f` is differentiable on the open unit ball `{z : ℂ | ‖z‖ < 1}`, and `‖f‖` attains a maximum
in  this open ball, then `f` is constant 

-   If `f` is a function differentiable on the open unit ball, and there exists an `r < 1` such that
any value of `‖f‖` on the open ball is bounded above by some value on the closed ball of radius `r`,
then `f` is constant. 

These lemmas together with #18192 will be used to prove some dimension results for spaces of modular forms.
TobiasLeichtfried pushed a commit that referenced this pull request Nov 21, 2024
We use the Maximum modulus principle to show that modular forms of non-positive weights are bounded by its value of some element of the upper half plane imaginary part at least 1/2.




Co-authored-by: Chris Birkbeck <c.birkbeck@ucl.ac.uk>
Co-authored-by: David Loeffler <d.loeffler.01@cantab.net>
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. t-number-theory Number theory (also use t-algebra or t-analysis to specialize)

Projects

None yet

Development

Successfully merging this pull request may close these issues.

6 participants