Number theory (NT) on the arXiv is a big section. In fact over the last two years, a little over 5700 papers have been posted there. Just for fun I wrote a Python program to help me find the most popular words in the titles and abstracts of the papers. Excluding common english words and common mathematical words such prove, function, and theorem, here are the top twenty keywords I found:
- prime
- group
- integer
- modular
- rational
- elliptic
- quadratic
- series
- polynomial
- zeta
- class
- bound
- galois
- algebraic
- abelian
- representation
- adic
- sequence
- diophantine
- linear
And how does this compare to algebraic geometry (AG), with almost the same number of papers posted?
- projective
- algebraic
- curve
- smooth
- moduli
- group
- complex
- variety
- surface
- rational
- degree
- field
- finite
- point
- real
- surface
- toric
- bundle
- dimension
- genus
What about rings and algebras (RA), one of my favourite areas with a little under half of the above categories?
- algebra
- finite
- group
- ring
- field
- module
- hopf
- matrix
- category
- commutative
- simple
- graded
- generated
- polynomial
- characteristic
- linear
- quantum
- ideal
- free
- dimension
Again, all of these were approximately over the last two years. The program was a little crude and might have made a mistake here or there but looking at the words it found these seem like an excellent approximation.