MixedMath - Recent Commentshttps://davidlowryduda.comDavid's personal blog.en-usCopyright David Lowry-Duda (2022) - All Rights Reserved.admin@davidlowryduda.comadmin@davidlowryduda.comMon, 07 Jul 2025 20:19:18 +0000Mon, 07 Jul 2025 20:19:18 +0000mixedmathapp/generate_rss.py v0.1https://cyber.harvard.edu/rss/rss.htmlhttps://davidlowryduda.com/static/images/favicon-32x32.pngMixedMathhttps://davidlowryduda.comDavid Lowry-Duda on Normalizations of murmurationshttps://davidlowryduda.com/normalizations-murmurations<p>The data is from the <a href="https://www.lmfdb.org/EllipticCurve/Q/">LMFDB</a>. I made these plots using code similar to that in <a href="/ecq-distinguishing/">my note on distinguishing sets of coefficients</a>. If you're interested in playing with the data, I suggest trying out <a href="https://www.lmfdb.org/api/options">the api options</a>. Let me (or other LMFDB people) know if you have trouble and we can help out.</p>f2cec97e078a889e9b46c0a60d48e678Thu, 12 Jun 2025 03:14:15 +0000Em on Normalizations of murmurationshttps://davidlowryduda.com/normalizations-murmurations<p>Where is the data for the plots? Can I download it?</p>f339df3c3380139c0484ca070f42255cMon, 09 Jun 2025 03:14:15 +0000Shiva on An intuitive overview of Taylor serieshttps://davidlowryduda.com/an-intuitive-overview-of-taylor-series<p>I was solving limits and continuity, and a question had always been in my mind. How did peeps actually derive the expansion of functions like $\sin(x)$, $\cos(x)$, $\log(1 + x)$, etc. I saw your comment about self referencing your blog from MathStackExchange. I checked out your explanation and it is literally perfect. Thank you.</p>ffe4f8cf8c77f37a99b61ba8f666d408Wed, 14 May 2025 03:14:15 +0000DLD on Paper: The Fibonacci Zeta Function and Continuationhttps://davidlowryduda.com/paper-fibonacci-i<p>We've now also uploaded our <a href="https://arxiv.org/abs/2502.01415">sequel paper</a> to the arxiv. In this paper, we focus on modular forms.</p>a3b0bc5fbe50e769e56f12edf1d6aebeWed, 05 Feb 2025 03:14:15 +0000DLD on Odd Fibonacci Zeta Functionhttps://davidlowryduda.com/odd-fibonacci<p>We've now also uploaded our <a href="https://arxiv.org/abs/2502.01415">sequel paper</a> to the arxiv. In this paper, we focus on modular forms.</p> <p>We promised this paper in the first paper.</p>6b4025275b6856ea8feb1c0590e93cffWed, 05 Feb 2025 03:14:15 +0000davidlowryduda on An (updated) brief note on cryptographyhttps://davidlowryduda.com/updated-note-on-cryptography<p>I should thank some readers for pointing out that my previous code was old and no longer ran. Cheers, and happy new year.</p>1c695bf439729594cc5628f8ee39b462Mon, 30 Dec 2024 03:14:15 +0000davidlowryduda on A brief notebook on cryptographyhttps://davidlowryduda.com/a-brief-notebook-on-cryptography<p>@anon You're right! This is very python2. I'll post an updated version right now. It's <a href="/updated-note-on-cryptography/">now here</a>.</p>0f81cae5a14dd09c3786d289fa3836b7Mon, 30 Dec 2024 03:14:15 +0000anon on A brief notebook on cryptographyhttps://davidlowryduda.com/a-brief-notebook-on-cryptography<p>I think this doesn't work with python3.10 anymore? I'm not familiar enough with OO languages to figure this out. Can you provide a solution?</p>bfa403191c3851ce50cb0b2f47b5af26Mon, 30 Dec 2024 03:14:15 +0000DLD on Odd Fibonacci Zeta Functionhttps://davidlowryduda.com/odd-fibonacci<blockquote> <p>I experiment with mirroring some commentary from Mastodon and here. This is from <a href="https://mathstodon.xyz/@davidlowryduda">@davidlowryduda@mathstodon</a>.</p> </blockquote> <p>The Dirichlet series $Z(s) = \sum F(n)^{-s}$ where $F(n)$ is the $n$th Fibonacci number has meromorphic continuation. And it looks pretty cool.</p>895b8f22592de9d62ac1ee4f90ea5730Wed, 04 Dec 2024 03:14:15 +0000DLD on Murmurations in Maass formshttps://davidlowryduda.com/maass-murmurations<p>As part of the <a href="https://cmsa.fas.harvard.edu/event/mml2024/">program in Mathematics and Machine Learning</a> at Harvard's CMSA, we looked further at what machine learning (both unsupervised and supervised) techniques have to say about Maass forms, murmurations style.</p> <p>Despite the data being transcendental and approximate, the machines can say a lot! We're going to have a preliminary talk about this during the closing workshop of the program in the coming week. (These talks are recorded &mdash; you can see a preview of our preprint in Edgar Costa's talk, and a preview of a different preprint in my talk).</p>f4eb1a4ad81a134f79770b6828531a8cFri, 25 Oct 2024 03:14:15 +0000David Lowry-Duda on Technical report on machine learning experiments for the Möbius functionhttps://davidlowryduda.com/ml-mobius-technical<p>All the code to run the experiments is here or in the Int2Int github repository I linked to. It's not as hard to run as it might look!</p> <p>I don't know what you mean about primes. But if you set up an experiment along these lines, I'd be interested to hear about it.</p>75f5f47d9d2f996a73694a1c25aae1b1Thu, 24 Oct 2024 03:14:15 +0000SH on Technical report on machine learning experiments for the Möbius functionhttps://davidlowryduda.com/ml-mobius-technical<p>Can you share the GPU code? Can you predict primes?</p>a38630d0c7a06f04fb75c92a2fcf7fc4Wed, 23 Oct 2024 03:14:15 +0000DLD on Explicit equations for cubic surfaceshttps://davidlowryduda.com/explicit-cubic-surfaces<p>Excellent observation! At first I thought a lot was lost by choosing the points to be $6$ points in $\mathbb{P}^2(\mathbb{F}_q)$ instead of consisting of Galois orbits. But actually passing to (at most) sextic extensions and doing the same analysis barely loses anything.</p> <p>The analysis is similar.</p> <p>This is an interesting heuristic. I wonder: can something like this be made rigorous?</p>77e5c66bed05c72bd2e556e70928ba7aThu, 26 Sep 2024 03:14:15 +0000anon on Explicit equations for cubic surfaceshttps://davidlowryduda.com/explicit-cubic-surfaces<p>Consider an analogous problem over $\mathbb{F}_q$. We first count the number of ''cubic surfaces'' here, i.e. homogeneous cubic $4$-variable polynomials over $\mathbb{F}/\mathbb{F}^\times$.</p> <p>There are $q^{20} - 1$ homogenous, four-variable cubic polynomials with coefficients in $\mathbb{F}$. The $20$ is a ''stars and bars game'' analysis. There are $3$ powers that we insert into $4$ regions, which can be done in ${4 + 3 - 1 \choose 3} = 20$ ways. Accounting for $\mathbb{F}^\times$ invariance, there are $M := (q^{20} - 1)/(q - 1) > q^{19}$ equivalence classes.</p> <p>Now suppose we want to count the number of choices of any $6$ <strong>rational</strong> points. The number of points in $\mathbb{P}^2(\mathbb{F}_q)$ is $n := (q^3 - 1)/(q-1) = q^2 + q + 1$. There are up to $N := {n \choose 6} \lesssim q^{12}$ many choices of $6$ points to construct blowups.</p> <p>Thus the probability that a random rational cubic surfaces comes "from blowing up $6$ points" in $\mathbb{P}^2(\mathbb{F}_q)$ is $< q^{-7}$, quite small.</p>ddf528243979cb3bb3a4bed71fbb4586Thu, 26 Sep 2024 03:14:15 +0000DLD on Murmurations in Maass formshttps://davidlowryduda.com/maass-murmurations<p>We've now proved a version of these murmurations. See <a href="https://arxiv.org/abs/2409.00765">this paper on the arxiv</a> for more.</p> <p>There is a miraculus aspect: the underlying murmuration function is the same as the function for <a href="https://arxiv.org/abs/2310.07746">modular murmurations in the weight aspect</a>. I have no satisfying explanation for this.</p>cb97a9186abbbf200534d406ea3d33e5Thu, 05 Sep 2024 03:14:15 +0000DLD on Maass forms in the LMFDBhttps://davidlowryduda.com/maass-forms-now-in-lmfdb<blockquote> <p>I experiment with mirroring some commentary from Mastodon and here. This is from <a href="https://mathstodon.xyz/@davidlowryduda">@davidlowryduda@mathstodon</a>.</p> </blockquote> <p>Rigorous Maass forms are now on the (beta) of the LMFDB! Go check them out.</p> <p>https://beta.lmfdb.org/ModularForm/GL2/Q/Maass/</p>4dcdc591fd742dfa47082f34230a8640Wed, 05 Jun 2024 03:14:15 +0000DLD on Another year, another TeXLive reinstallationhttps://davidlowryduda.com/another-year-another-texlive<blockquote> <p>I experiment with mirroring some commentary from Mastodon and here. This is from <a href="https://mathstodon.xyz/@davidlowryduda">@davidlowryduda@mathstodon</a>.</p> </blockquote> <p>Once a year, sometime shortly after March, I try to update something with <code>tlmgr</code> (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.</p> <p>Then I spend 30 minutes updating my texlive.</p> <p>And then <em>afterwards</em> I can install the random latex package I needed.</p> <p>Today is that day for me. And the package was extdash.</p> <p>I do essentially the same steps every year. This year I put these steps in a public place.</p>c82a50f5c5ceff302f8ea93e78f79111Mon, 15 Apr 2024 03:14:15 +0000DLD on FLT3 at LftCM2024https://davidlowryduda.com/flt3-at-lftcm2024<p>Thank you to Edward van de Meent and Riccardo Brasca for comments and pointing out errors in earlier versions of this post.</p>81694b0804ac4a835f7465ef1a180c52Tue, 02 Apr 2024 03:14:15 +0000DLD on FLT3 at LftCM2024https://davidlowryduda.com/flt3-at-lftcm2024<blockquote> <p>I experiment with mirroring some commentary from Mastodon and here. This is from <a href="https://mathstodon.xyz/@davidlowryduda">@davidlowryduda@mathstodon</a>.</p> </blockquote> <p>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 <em>good way</em> in Lean.</p> <p>I wrote a bit more about this experience.</p>4707fb71daeb6011c3bfb73ed27beebeTue, 02 Apr 2024 03:14:15 +0000DLD on Zeros of Dirichlet Series IVhttps://davidlowryduda.com/zeros-of-dirichlet-series-iv<p>Thank you! I've fixed the typo.</p> <p>I haven't published these yet. I'm going to try to put this in a publishable form in the next couple of months.</p>c92ce204cb6bf35b76b1d5a2072cf5b8Wed, 06 Mar 2024 03:14:15 +0000DLD on Quanta on Murmurationshttps://davidlowryduda.com/quanta-on-murmurations<blockquote> <p>I experiment with mirroring some commentary from Mastodon and here. This is from <a href="https://mathstodon.xyz/@davidlowryduda">@davidlowryduda@mathstodon</a>.</p> </blockquote> <p>Quanta wrote an article on murmurations that mentions the work of my collaborators Bober, Booker, Lee, and I.</p> <p>We're not the focus, but we're there - and that's pretty cool. Check it out.</p> <p>I hope to announce another paper in the same direction in the next couple of weeks, too.</p>d83c5e80417edd57aa712f488c7fcf27Tue, 05 Mar 2024 03:14:15 +0000Chris on Zeros of Dirichlet Series IVhttps://davidlowryduda.com/zeros-of-dirichlet-series-iv<p>Have you published this yet? There is a typo in the second display equation. It should have a $\Lambda$ instead of a $\lambda$.</p>92cf0eaf79ad6553f40d4435930dfd71Tue, 05 Mar 2024 03:14:15 +0000PJ on Paper: Congruent number triangles with the same hypotenusehttps://davidlowryduda.com/paper-congruent-triangles-same-hypotenuse<p>@RB can't find more. You already found them all</p>33e5fc6e8f9c1af973871e399c59f88eThu, 15 Feb 2024 03:14:15 +0000DLD on Paper: Towards a Classification of Isolated $j$-invariantshttps://davidlowryduda.com/paper-isolated-j-invariants<p>I'll give a small update as a comment. Our paper has been accepted and will appear in <em>Mathematics of Computation</em> shortly. (And <em>Math Comp</em> was very fast and forthright with their review, which is nice).</p>0e93676137e85e8832a8c81d8376ed06Wed, 14 Feb 2024 03:14:15 +0000David Lowry-Duda on Examining Excess in the Schmidt Boundhttps://davidlowryduda.com/schmidt-experiment<p>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.</p> <p>The setup and conclusion are more complicated. But the conclusion is the same. So I chose to not document or include it.</p>949e5daee523c8d6ec9629f717261c7bTue, 13 Feb 2024 03:14:15 +0000