<p>Fun fact: mathematical disciplines blend at the graduate level. If you want to be a number theorist, you’ll be exposed to a fair bit of analysis. Better start getting used to it. </p>
<p>Every graduate program in the country will either test you or require coursework on measure theory and functional analysis. If you want to avoid all analysis beyond that, you’d have to hide in specialties dealing with very finite and discrete objects, like combinatorics. (Though there are analytical tools used in combinatorics as well…)</p>