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### Recent Posts

- 2024-11-13 - Slides from a talk at the Simons Center for Geometry and Physics on Murmurations and trace formulas
- 2024-10-29 - Slides from a talk at Harvard on Machine Learning and the Möbius Function
- 2024-10-19 - Technical report on machine learning experiments for the Möbius function
- 2024-10-19 - General report on machine learning experiments for the Möbius function
- 2024-10-18 - Numerically computing Petersson inner products and $L$-function residues
- 2024-10-18 - code4math research community: call for contributors
- 2024-09-27 - Fourier expansions at different cusps
- 2024-09-20 - Explicit equations for cubic surfaces

### Recent Comments

- (2024-10-25) DLD wrote on Murmurations in Maass forms: As part of the [program in Mathematics and Machine Learning](https://cmsa.fas.harvard.edu/event/mml2024/) at Harvard's CMSA, we looked further at what machine learning (both unsupervised and[...]
- (2024-10-24) David Lowry-Duda wrote on Technical report on machine learning experiments for the Möbius function: 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! I don't know what you mean about primes. But if you set up[...]
- (2024-10-23) SH wrote on Technical report on machine learning experiments for the Möbius function: Can you share the GPU code? Can you predict primes?
- (2024-09-26) DLD wrote on Explicit equations for cubic surfaces: 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[...]
- (2024-09-26) anon wrote on Explicit equations for cubic surfaces: 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[...]
- (2024-09-05) DLD wrote on Murmurations in Maass forms: We've now proved a version of these murmurations. See [this paper on the arxiv](https://arxiv.org/abs/2409.00765) for more. There is a miraculus aspect: the underlying murmuration function is[...]
- (2024-06-05) DLD wrote on Maass forms in the LMFDB: > I experiment with mirroring some commentary from Mastodon and here. This is > from [@davidlowryduda@mathstodon](https://mathstodon.xyz/@davidlowryduda). Rigorous Maass forms are now on the[...]
- (2024-04-15) DLD wrote on Another year, another TeXLive reinstallation: > I experiment with mirroring some commentary from Mastodon and here. This is > from [@davidlowryduda@mathstodon](https://mathstodon.xyz/@davidlowryduda). Once a year, sometime shortly after[...]

### All blog posts

- 2024-11-13 - Slides from a talk at the Simons Center for Geometry and Physics on Murmurations and trace formulas
- 2024-10-29 - Slides from a talk at Harvard on Machine Learning and the Möbius Function
- 2024-10-19 - Technical report on machine learning experiments for the Möbius function
- 2024-10-19 - General report on machine learning experiments for the Möbius function
- 2024-10-18 - Numerically computing Petersson inner products and $L$-function residues
- 2024-10-18 - code4math research community: call for contributors
- 2024-09-27 - Fourier expansions at different cusps
- 2024-09-20 - Explicit equations for cubic surfaces
- 2024-09-10 - Hecke Algebra details
- 2024-07-24 - A note on sums over primes
- 2024-06-05 - Maass forms in the LMFDB
- 2024-04-15 - Another year, another TeXLive reinstallation
- 2024-03-30 - FLT3 at LftCM2024
- 2024-03-05 - Quanta on Murmurations
- 2024-02-21 - Not quite 3 and a half years
- 2024-02-13 - Examining Excess in the Schmidt Bound
- 2024-01-16 - Bounds on partial sums from functional equations
- 2023-11-15 - Paper: Towards a Classification of Isolated $j$-invariants
- 2023-11-14 - Paper: Congruent number triangles with the same hypotenuse
- 2023-11-13 - Bringing back the blogroll
- 2023-10-21 - Paper: Murmurations of modular forms in the weight aspect
- 2023-07-19 - Murmurations in Maass forms
- 2023-02-23 - Slides from a talk at Concordia University
- 2023-01-27 - Paper: Sums of cusp forms coefficients along quadratic sequences
- 2023-01-01 - On Mathstodon
- 2022-12-07 - Implementation notes on modular curve visualizations
- 2022-12-02 - Slides on Maass forms, nearing completion
- 2022-11-09 - Slides on Modular Forms and the L-functions, a talk at the Simons Center for Geometry and Physics
- 2022-11-03 - Supplement to Langlands survey
- 2022-11-02 - Notes from a survey talk by Jeff Lagarias on the Collatz problem
- 2022-10-17 - Paul R. Halmos -- Lester R. Ford Award
- 2022-10-15 - Slides from a talk at Maine-Quebec
- 2022-07-22 - Initial thoughts on visualizing number fields
- 2022-07-20 - Computing coset representatives for quotients of congruence subgroups
- 2022-07-09 - Note Series on Zeros of General Dirichlet Series
- 2022-07-08 - Zeros of Dirichlet Series IV
- 2022-07-07 - Zeros of Dirichlet Series III
- 2022-06-01 - Visualizations for Quanta's 'What is the Langlands Program?'
- 2022-05-09 - Slides from a talk on Improved Bounds for Number Fields
- 2022-04-30 - Simplified proofs and reasoning in "Improved Bounds on Number Fields of Small Degree"
- 2022-04-28 - Paper: Counting number fields of small degree
- 2022-04-02 - Comments on this site
- 2022-03-28 - Plaintext Email
- 2022-03-24 - Slides from a talk: Computing and verifying Maass forms
- 2022-03-23 - Slides from a talk: How computation and experimentation inform research
- 2022-02-11 - colormapplot - like phasematplot, but with colormaps
- 2022-01-24 - Zeros of Dirichlet Series II
- 2022-01-20 - Zeros of Dirichlet Series
- 2021-12-07 - On van der Waerden's Conjecture
- 2021-11-06 - Slides from a talk on Quantitative Hilbert Irreducibility
- 2021-10-30 - Project Report on "Prime Sums"
- 2021-10-02 - Slides from a talk at Maine-Québec
- 2021-08-02 - Slides from a talk at Bridges 2021
- 2021-07-09 - Paper: Quantitative HIT and Almost Prime Polynomial Discriminants
- 2021-05-18 - Slides from a talk on Visualizing Modular Forms
- 2021-04-13 - Trace form 3.32.a.a
- 2021-03-22 - Slides from a talk on Half Integral Weight Dirichlet Series
- 2021-03-01 - Setting up a Wacom Intuos CTL-4100 drawing tablet on Ubuntu 20.04 LTS
- 2021-03-08 - A balancing act in "Uniform bounds for lattice point counting"
- 2021-02-17 - Slides from a talk at AIM
- 2021-02-10 - Slides from a talk on computing Maass forms
- 2020-12-04 - Long live opalstack!
- 2020-12-04 - Talk on computing Maass forms
- 2020-08-19 - The current cover art for the Proceedings of the Royal Society
- 2020-08-07 - phase_mag_plot: a sage package for plotting complex functions
- 2020-06-01 - Notes from a talk at Dartmouth on the Fibonacci zeta function
- 2020-05-13 - Pictures of equidistribution - the line
- 2020-05-05 - Points on $X^2 + Y^2 = 2$ equidistribute with respect to height
- 2019-12-06 - Proposal for new images for modular forms on the LMFDB
- 2019-11-22 - Notes behind a talk: visualizing modular forms
- 2019-11-05 - Making Plots of Modular Forms
- 2019-10-18 - Non-real poles and irregularity of distribution I
- 2019-10-05 - Notes from a talk at the Maine-Quebec Number Theory Conference
- 2019-07-05 - The Insidiousness of Mathematics
- 2019-06-28 - Another proof of Taylor's Theorem
- 2019-06-12 - Email configuration for mutt on a webfaction server
- 2019-06-05 - Choosing functions and generating figures for "When are there continuous choices for the mean value abscissa?"
- 2019-06-04 - Paper: When are there continuous choices for the Mean Value Abscissa?
- 2019-04-03 - How do we decide how many representatives there are for each state?
- 2019-03-28 - African clawed frog
- 2019-02-25 - Notes from a talk: Finding Congruent Numbers, Arithmetic Progressions of Squares, and Triangles
- 2019-02-22 - Writing a Python Script to be Used in Vim
- 2019-01-18 - Slides for a talk at JMM 2019
- 2018-12-07 - Update to Second Moments in the Generalized Gauss Circle Problem
- 2018-11-10 - The wrong way to compute a sum: addendum
- 2018-11-02 - The wrong way to compute a sum
- 2018-10-09 - Using lcalc to compute half-integral weight L-functions
- 2018-09-14 - Extra comparisons in Python's timsort
- 2018-09-06 - Speed talks should be at every conference
- 2018-07-28 - A bookmarklet to inject colorblind friendly CSS into Travis CI
- 2018-07-28 - Seeing color shouldn't feel like a superpower
- 2018-07-18 - Notes from a Talk at Building Bridges 4
- 2018-05-11 - Splitting Easy MathSE Questions into a New NoviceMathSE Is a Bad Idea
- 2018-05-01 - Ghosts of Forums Past
- 2018-04-24 - Challenges facing community cohesion (and Math.StackExchange in particular)
- 2018-04-13 - Paper: A Shifted Sum for the Congruent Number Problem
- 2018-04-09 - Cracking Codes with Python: A Book Review
- 2018-03-21 - Notes from a talk at Tufts, Automorphic Forms Workshop
- 2018-03-04 - Hosting a Flask App on WebFaction on a Non-root Domain
- 2018-02-03 - Segregation, Gerrymandering, and Schelling's Model
- 2018-01-24 - The Hawaiian Missile Crisis
- 2018-01-10 - Slides from a talk at the Joint Math Meetings 2018
- 2018-01-04 - We begin bombing Korea in five minutes: Parallels to Reagan in 1984
- 2017-11-02 - A Jupyter Notebook from a SageMath tutorial
- 2017-10-07 - Having no internet for four half weeks isn't necessarily all bad
- 2017-09-22 - A Short Note on Gaps Between Powers of Consecutive Primes
- 2017-07-20 - Sage Days 87 Demo: Interfacing between sage and the LMFDB
- 2017-05-26 - Paper: Second moments in the generalized Gauss circle problem
- 2017-05-21 - How fat would we have to get to balance carbon emissions?
- 2017-04-21 - Slides from a Dissertation Defense
- 2017-04-11 - pstricks
- 2017-04-11 - Experimenting with latex2html5: PSTricks to HTML interactivity
- 2017-03-29 - Slides from a Talk at the Dartmouth Number Theory Seminar
- 2017-03-11 - Smooth Sums to Sharp Sums
- 2017-01-21 - About 2017
- 2017-01-07 - Revealing zero in fully homomorphic encryption is a Bad Thing
- 2016-12-21 - Math 100 - Concluding Remarks
- 2016-12-04 - Computing pi with tools from calculus
- 2016-10-25 - Series convergence tests with prototypical examples
- 2016-10-04 - A notebook preparing for a talk at Quebec-Maine
- 2016-09-29 - Math 100 - Completing the partial fractions example from class
- 2016-08-12 - Paper: On Functions Whose Mean Value Abscissas are Midpoints, with Connections to Harmonic Functions (with Paul Carter)
- 2016-06-03 - Paper: Sign Changes of Coefficients and Sums of Coefficients of Cusp Forms
- 2016-05-25 - Math 42 Spring 2016 Student Showcase
- 2016-05-20 - Math 42 - Concluding Remarks
- 2011-04-13 - Math 420 - Supplement on Gaussian integers II
- 2016-04-10 - Math 420 - Supplement on Gaussian integers
- 2016-03-22 - A brief notebook on cryptography
- 2016-03-12 - Motivating a change of variables in $\int \log x / (x^2 + ax + b) dx$
- 2016-02-04 - Math 420 - Second Week
- 2016-01-28 - Math 420 - First week homework and references
- 2016-01-02 - Paper: Short-integral averages of sums of Fourier coefficients of Cusp Forms
- 2015-12-04 - Paper: The second moments of sums of Fourier coefficients of cusp forms
- 2015-06-13 - Estimating the number of squarefree integers up to $X$
- 2015-05-10 - Some statistics on the growth of Math.SE
- 2014-11-20 - One integral served two ways
- 2014-11-12 - The gamma function, beta function, and duplication formula
- 2014-11-05 - Notes from a talk - On the Mean Value Theorem
- 2014-10-29 - Three Conundrums on Infinity
- 2014-10-22 - Continuity of the Mean Value Abscissa
- 2014-10-14 - Review of How Not to be Wrong by Jordan Ellenberg
- 2014-10-07 - Another proof of Wilson's Theorem
- 2014-09-29 - Trigonometric and related substitutions in integrals
- 2014-09-22 - A bit more about partial fraction decomposition
- 2011-04-08 - On least squares - a question from reddit
- 2014-11-16 - Friendly introduction to sieves with a look towards recent progress
- 2013-12-30 - Math 100 - Concluding Remarks
- 2013-12-12 - On the identity $1 + 2 + \ldots = -1/12$
- 2013-11-16 - An intuitive overview of Taylor series
- 2013-11-11 - Understanding $\int_{-\infty}^\infty \frac{\mathrm{d}t}{(1 + t^2)^n}$
- 2013-11-07 - Math 100 - before second midterm
- 2013-09-28 - Math 100 - Week 4
- 2013-09-24 - Math 199 - Week 3 and pre-midterm
- 2013-09-10 - Happy Birthday to the Science Guy
- 2013-09-07 - An intuitive introduction to calculus
- 2013-08-02 - Twenty Mathematicians, Two Hard Problems, One Week, IdeaLab2013
- 2013-07-09 - Chinese Remainder Theorem -SummerNT
- 2013-07-01 - Notes on the first week - SummerNT
- 2013-06-24 - A proof from the first sheet - SummerNT
- 2013-05-21 - Recent developments in twin primes, Goldbach, and Open Access
- 2013-04-24 - Calculations with a Gauss-type sum
- 2013-02-08 - Hurwitz zeta is a sum of Dirichlet $L$-functions, and vice-versa
- 2013-01-18 - Math journals and the fight over open access
- 2013-02-16 - A Book Review of Count Down - The race for beautiful solutions at the IMO
- 2013-01-12 - Are the calculus MOOCs any good - after week 1
- 2013-01-08 - Are the calculus MOOCs any good?
- 2012-12-30 - Math 90 - Concluding Remarks
- 2012-11-18 - Math 90 - Week 11
- 2012-11-07 - Math 90 - Week 9
- 2012-11-08 - An application of Mobius inversion to certain Asymptotics
- 2012-10-24 - Math 90 - Week 8 Quiz
- 2012-10-24 - Math 90 - Week 8
- 2012-10-17 - Math 90 - Week 7
- 2012-10-03 - Math 90 - Week 5
- 2012-09-28 - Math 90 - Week 4
- 2012-09-19 - Math 90 - Week 3
- 2012-09-11 - Math 90 - Week 2
- 2012-09-04 - Math 90 - Week 1
- 2012-08-24 - The danger of confusing cosets and numbers
- 2012-08-23 - An elementary proof of when 2 is a quadratic residue
- 2012-08-11 - Dancing ones PhD
- 2012-08-09 - Precalculus Supplement - Synthetic Division
- 2012-06-21 - A MSE collection - topology book references
- 2012-06-11 - A MSE Collection - a list of integrals
- 2012-06-15 - Three number theory bits - One elementary, the 3-Goldbach, and ABC
- 2012-04-26 - A pigeon for every hole, and then one (sort of)
- 2012-04-16 - From the exchange - is it unheard of to like math but hate proofs?
- 2011-12-24 - Education Musings
- 2011-12-10 - Tiontobl - a combinatorial game
- 2011-12-06 - Mapping class groups summary
- 2011-12-02 - Ghostwritten Word
- 2011-11-24 - Points under a parabola
- 2011-11-21 - Two short problems
- 2011-10-23 - A new toy problem
- 2011-10-22 - Reading Math
- 2011-09-21 - A month, you say?
- 2011-08-07 - Fermat Factorization II
- 2011-07-28 - From the Exchange
- 2011-07-26 - Factoring III
- 2011-07-25 - Prime rich and prime poor
- 2011-07-25 - Factoring II
- 2011-07-23 - Giving Journals
- 2011-06-06 - The Collatz Conjecture - recent development?
- 2011-05-27 - Visiting Gaussian Quadrature
- 2011-05-24 - Daily Math in Zagreb
- 2011-05-12 - Integration by Parts
- 2011-04-20 - Khan an effective supplement, a survey
- 2011-04-20 - Towards an expression for pi
- 2011-05-27 - Factoring I
- 2011-04-14 - 2401 - Additional examples for test 3
- 2011-04-13 - Slow factoring algorithm II
- 2011-04-08 - Blue Eyes and Brown Eyes
- 2011-04-07 - An even later pi day post
- 2011-04-07 - An interesting (slow) factoring algorithm
- 2011-03-31 - Perfect Partitions II
- 2011-03-28 - Perfect Partitions
- 2011-03-27 - About 3 weeks behind silly hype
- 2011-03-26 - A lite pi day post
- 2011-03-29 - A bag's journey in search of its owner
- 2011-03-24 - Containers of Water II
- 2011-03-23 - 2401 - Missing recitation
- 2011-03-22 - Containers of Water - maybe an interesting question
- 2011-04-08 - Test Solution
- 2011-03-20 - Pizza
- 2011-03-20 - Fun limit
- 2011-03-20 - Math - dealing with sin (and cos) every day