[Merged by Bors] - feat(NumberTheory/ModularForms): two-variable Jacobi theta#9666
Closed
[Merged by Bors] - feat(NumberTheory/ModularForms): two-variable Jacobi theta#9666
Conversation
CBirkbeck
reviewed
Jan 12, 2024
CBirkbeck
reviewed
Jan 12, 2024
| set_option linter.uppercaseLean3 false in | ||
| #align real.is_Theta_exp_comp_one Real.isTheta_exp_comp_one | ||
|
|
||
| lemma summable_exp_neg_nat : Summable (fun n : ℕ ↦ exp (-n)) := by |
Contributor
There was a problem hiding this comment.
Maybe generalize this to exp (-n * x) with positive x? I'd expect this to be more useful than the special case x = 1.
Contributor
Author
There was a problem hiding this comment.
Good point, I added a lemma showing that Summable (fun n : ℕ ↦ exp (n * a)) ↔ a < 0 and deduced the case at hand from this.
MichaelStollBayreuth
approved these changes
Jan 14, 2024
Contributor
MichaelStollBayreuth
left a comment
There was a problem hiding this comment.
LGTM! I'm looking forward to Dirichlet L-series as entire functions, functional equation and all...
Co-authored-by: Michael Stoll <99838730+MichaelStollBayreuth@users.noreply.github.com>
Co-authored-by: Chris Birkbeck <c.birkbeck@uea.ac.uk>
Contributor
Author
|
@riccardobrasca Hi Riccardo, this should be ready now |
riccardobrasca
approved these changes
Jan 17, 2024
Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com>
…thlib4 into DL_jacobi_twovar
Collaborator
|
LGTM |
Member
|
Thanks! bors d+ |
Contributor
|
✌️ loefflerd can now approve this pull request. To approve and merge a pull request, simply reply with |
Contributor
Author
|
bors r+ |
mathlib-bors bot
pushed a commit
that referenced
this pull request
Jan 17, 2024
Add a more general version of the Jacobi theta function with a second variable, and prove the transformation law for this more general function rather than just for the one-variable version. Preparatory to functional equations for Dirichlet L-functions.
Contributor
|
Pull request successfully merged into master. Build succeeded: |
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
4 participants
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.
Add a more general version of the Jacobi theta function with a second variable, and prove the transformation law for this more general function rather than just for the one-variable version. Preparatory to functional equations for Dirichlet L-functions.