In the previous post we defined $latex {p}&fg=000000$-adic numbers. This post will state (mostly without proof) some more surprising results about continuous functions $latex {f \colon \mathbb Z_p \rightarrow \mathbb Q_p}&fg=000000$. Then we give the famous proof of the Skolem-Mahler-Lech theorem using $latex {p}&fg=000000$-adic analysis. 1. Digression on $latex {\mathbb C_p}&fg=000000$ Before I go on,… Continue reading A trailer for p-adic analysis, second half: Mahler coefficients

# Tag: technical

## A trailer for p-adic analysis, first half: USA TST 2003

I think this post is more than two years late in coming, but anywhow... This post introduces the $latex {p}&fg=000000$-adic integers $latex {\mathbb Z_p}&fg=000000$, and the $latex {p}&fg=000000$-adic numbers $latex {\mathbb Q_p}&fg=000000$. The one-sentence description is that these are ``integers/rationals carrying full mod $latex {p^e}&fg=000000$ information'' (and only that information). The first four sections will… Continue reading A trailer for p-adic analysis, first half: USA TST 2003

## A story of block-ascending permutations

I recently had a combinatorics paper appear in the EJC. In this post I want to brag a bit by telling the ``story'' of this paper: what motivated it, how I found the conjecture that I originally did, and the process that eventually led me to the proof, and so on. This work was part… Continue reading A story of block-ascending permutations

## DNSCrypt Setup with PDNSD

Here are notes for setting up DNSCrypt on Arch Linux, using pdnsd as a DNS cache, assuming the use of NetworkManager. I needed it one day since the network I was using blocked traffic to external DNS servers (parental controls), and the DNS server provided had an outdated entry for hmmt.co. (My dad then pointed… Continue reading DNSCrypt Setup with PDNSD

## Shifting PDF’s using gs

Some time ago I was reading the 18.785 analytic NT notes to try and figure out some sections of Davenport that I couldn't understand. These notes looked nice enough that I decided I should probably print them out, But much to my annoyance, I found that almost all the top margins were too tiny, and… Continue reading Shifting PDF’s using gs

## Git Aliases

For Git users: I've recently discovered the joy that is git aliases, courtesy of this blog post. To return to the favor, I thought I'd share the ones that I came up with. For those of you that don't already know, Git allows you to make aliases -- shortcuts for commands. Specifically, if you add… Continue reading Git Aliases