Freedom Math Dance
A blog about math (mainly), computer tricks (sometimes) and jazz music.
Wednesday, May 13, 2020
Using texexec to modify a PDF file (from the shell)
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We all regularly have to modify a PDF file, either taking a part of it. The texexec program which is shipped with ConTeXt allows to do most...
Sunday, April 12, 2020
Some proofs of the quadratic reciprocity law
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Gauss's quadratic reciprocity law is a mysterious relation between prime numbers. If $p$ and $q$ are distinct prime numbers, it shows t...
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Wednesday, February 12, 2020
Dynamics of Hecke correspondences
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This morning, Sebastián Herrero, Ricardo Menares and Juan Rivera-Letelier released a preprint on the arXiv entitled “ p-Adic distribution of...
Friday, December 27, 2019
Behaviour of conjugacy by reduction modulo integers
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Let $A$ and $B\in\mathrm{M}_n(\mathbf Z)$ be two square matrices with integer coefficients. Assume that they are conjugate by $\mathrm{GL}_n...
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Tuesday, July 2, 2019
Irreducibility of cyclotomic polynomials
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For every integer $n\geq 1$, the $n$th cyclotomic polynomial $\Phi_n$ is the monic polynomial whose complex roots are the primitive $n$th ro...
3 comments :
Sunday, May 19, 2019
Designs, Skolem sequences, and partitions of integers
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Recently, my father offered me the first volume of a graphic novel by Jean-François Kierzkowski and Marek called La suite de Skolem — Skole...
Saturday, May 12, 2018
A theorem of Lee—Yang on root of polynomials
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A recent MathOverflow post asked for a proof that the roots of certain polynomials were located on the unit circle. A comment by Richard St...
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