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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
10
votes
Brief Introduction to Modular Forms
Perhaps it is a little too brisk for your purposes, but I have always liked Zagier's exposition in The 1-2-3 of Modular Forms (Springer Universitext) very much. It is about 100 pages, more than half …
3
votes
Is $(p^2-1)/2$ never squarefull when $p > 3$ is a Mersenne prime?
Well, maybe I'm missing the point, but the first Mersenne prime is $3=2^2-1$, and $\frac{3^2-1}{2} = 4 = 2^2$, so... no, I guess.