MixedMath - Recent Comments

DLD on Another year, another TeXLive reinstallation

Mon, 15 Apr 2024 03:14:15 +0000

I experiment with mirroring some commentary from Mastodon and here. This is from @davidlowryduda@mathstodon.

Once a year, sometime shortly after March, I try to update something with tlmgr (the texlive manager) and it flails about. It tells me that I'm silly for not noticing that TeXLive has advanced another year, and that I should get with the times and update too.

Then I spend 30 minutes updating my texlive.

And then afterwards I can install the random latex package I needed.

Today is that day for me. And the package was extdash.

I do essentially the same steps every year. This year I put these steps in a public place.

DLD on FLT3 at LftCM2024

Tue, 02 Apr 2024 03:14:15 +0000

Thank you to Edward van de Meent and Riccardo Brasca for comments and pointing out errors in earlier versions of this post.

DLD on FLT3 at LftCM2024

Tue, 02 Apr 2024 03:14:15 +0000

I experiment with mirroring some commentary from Mastodon and here. This is from @davidlowryduda@mathstodon.

I attended Lean for the Curious Mathematician 2024 at CIRM. Along with Riccardo Brasca, Sanyam Gupta, Omar Haddad, Lorenzo Luccioli, Pietro Monticone, Alexis Saurin, and Florent Schaffhauser, we proved the $n=3$ case of Fermat's Last Theorem in a good way in Lean.

I wrote a bit more about this experience.

DLD on Zeros of Dirichlet Series IV

Wed, 06 Mar 2024 03:14:15 +0000

Thank you! I've fixed the typo.

I haven't published these yet. I'm going to try to put this in a publishable form in the next couple of months.

DLD on Quanta on Murmurations

Tue, 05 Mar 2024 03:14:15 +0000

I experiment with mirroring some commentary from Mastodon and here. This is from @davidlowryduda@mathstodon.

Quanta wrote an article on murmurations that mentions the work of my collaborators Bober, Booker, Lee, and I.

We're not the focus, but we're there - and that's pretty cool. Check it out.

I hope to announce another paper in the same direction in the next couple of weeks, too.

Chris on Zeros of Dirichlet Series IV

Tue, 05 Mar 2024 03:14:15 +0000

Have you published this yet? There is a typo in the second display equation. It should have a $\Lambda$ instead of a $\lambda$.

PJ on Paper: Congruent number triangles with the same hypotenuse

Thu, 15 Feb 2024 03:14:15 +0000

@RB can't find more. You already found them all

DLD on Paper: Towards a Classification of Isolated $j$-invariants

Wed, 14 Feb 2024 03:14:15 +0000

I'll give a small update as a comment. Our paper has been accepted and will appear in Mathematics of Computation shortly. (And Math Comp was very fast and forthright with their review, which is nice).

David Lowry-Duda on Examining Excess in the Schmidt Bound

Tue, 13 Feb 2024 03:14:15 +0000

I will also note that I hadn't expected this to be so cut and dry, and I ran a separate experiment that sampled randomly from the space of polynomials and went in that direction.

The setup and conclusion are more complicated. But the conclusion is the same. So I chose to not document or include it.

David Lowry-Duda on Examining Excess in the Schmidt Bound

Tue, 13 Feb 2024 03:14:15 +0000

I experiment with mirroring some commentary from Mastodon and here. This is from @davidlowryduda@mathstodon.xyz.

I study excess in the Schmidt bound for number fields. Schmidt estimated that there are at most $X^{\frac{n + 2}{4}}$ number fields of degree $n$ with discriminant up to $X$. But we expect the real number is really of the form $cX$ for some constant $c$.

To do this, Schmidt gives a region of polynomials to count, where some polynomial is guaranteed to generate each number field of discriminant up to $X$. There are two sorts of error there: counting polynomials that yield number fields with discriminant larger than $X$, and sets of polynomials that all count the same number field.

Which error is larger?

For heuristic reasons, we should expect counting polynomials that are too large to be a major source of overcounting. So perhaps a meaningful question would be: does counting the same number field multiple times account for much of the error at all?

In this note I describe an experiment and show that no, repeated counting isn't a significant factor.

DLD on Plaintext Email

Wed, 24 Jan 2024 03:14:15 +0000

I use K-9 on mobile, and a variety of clients on various machines.

The mobile app for gmail cannot send plaintext. By default, the web interface doesn't — but it can.

Plaintext is worse for marketing. You can't hide links or track image loading for additional analytics, so it is maybe no surprise that ad-based companies default to HTML email.

gmailer on Plaintext Email

Tue, 23 Jan 2024 03:14:15 +0000

What email do you use? gmail doesn't use plaintext?

David Lowry-Duda on Bounds on partial sums from functional equations

Thu, 18 Jan 2024 03:14:15 +0000

I experiment with mirroring some commentary from Mastodon and here. This is from @davidlowryduda@mathstodon.xyz.

In my first public note of the year, I comment on applying Landau's method to partial sums of full and half integral weight modular forms. This is where one uses a combinations of smoothed sums $\sum_{n \leq X} a(n) (n - X)^k$ to find reasonable bounds for the sharp sum $\sum_{n \leq X} a(n)$.

Implicitly, this note compares what one can do from my paper with Thorne and Taniguchi against my sequence of papers with Hulse, Kuan, and Walker — and identifies where there is hope to get better results in the future.

For additional context: I've been interested in improving these bounds since 2016. I've now studied the primary bound of $\sum_{n \leq X} a(n)$ in several different ways, and they all produce the same bound. This hints at some true barrier to our understanding, but I don't actually understand what this is.

DLD on Comments on this site

Wed, 15 Nov 2023 03:14:15 +0000

Yes, your message came through just fine. For a typical message, it's easy to extract plain messages from email. If someone were to try to send formatted content inside an HTML email, that might be a problem.

I use a couple of different email programs depending on context. See useplaintext.email for more precise software recommendations that I also generically support.

Sarah on Comments on this site

Mon, 13 Nov 2023 03:14:15 +0000

What email do you use? Gmail doesn't support plain email? Did this comment go through?

DLD on Paper: Congruent number triangles with the same hypotenuse

Wed, 01 Nov 2023 03:14:15 +0000

Good luck! I'll note that the sparseness means that it is extremely unlikely that a naive search, even very efficiently coded, would beat the approach guided by elliptic curves I describe in the paper. But I would be very interested to know a counterexample (if it exists) or a proof (if it exists) to my conjecture.

RB on Paper: Congruent number triangles with the same hypotenuse

Wed, 01 Nov 2023 03:14:15 +0000

Ah, I missed "primitive" so I will go back to my GP-Pari routines, since I have an efficient way of finding square pairs summing to a third square.

DLD on Paper: Congruent number triangles with the same hypotenuse

Wed, 01 Nov 2023 03:14:15 +0000

Thank you for your comment RB. The conjecture refers to primitive triangles for exactly this reason. The description above now includes your example in the description.

RB on Paper: Congruent number triangles with the same hypotenuse

Wed, 01 Nov 2023 03:14:15 +0000

David, the triangles $(740, 777, 1073)$ and $(348, 1015, 1073)$ both have the same hypotenuse. They both have the same non-square area $210$. In your paper you say these triangles do not exist? Did I miss something?

davidlowryduda on Initial thoughts on visualizing number fields

Thu, 02 Mar 2023 03:14:15 +0000

At CIRM in Luminy, a great alternative idea was proposed. The idea is to replicate parts of Mumford's famous picture on $\mathrm{Spec}(\mathbb{Z}[x])$, but presumably focus on only a single horizontal line (which corresponds to a fixed number field). This would display splitting behavior of various primes with some sort of line plot.

I think this is worth checking out!

davidlowryduda on Slides from a talk at Concordia University

Wed, 01 Mar 2023 03:14:15 +0000

I mean compute an arbitrarily close approximation here. And I should note that there are a fixed set of Maass forms with eigenvalues in some range $\frac{1}{4} < \lambda < \lambda_2$, so there are a precise list of forms that I am trying to find close approximations to.

AA on Slides from a talk at Concordia University

Wed, 01 Mar 2023 03:14:15 +0000

What does it mean to compute something that is uncomputable?

DLD on On Mathstodon

Mon, 02 Jan 2023 03:14:15 +0000

@davidlowryduda@mathstodon.xyz.

PD on Making Plots of Modular Forms

Mon, 02 Jan 2023 03:14:15 +0000

Thanks for the quick reply and your code! I was working already with few libs.

DLD on Making Plots of Modular Forms

Mon, 02 Jan 2023 03:14:15 +0000

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