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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Averaging the Mobius function on arithmetic progressions
The Mobius function $\mu\colon \mathbb{N}\to\{-1,0,1\}$ is given by $\mu(n)=(-1)^{k}$ if $n$ is the product of $k$ distinct prime numbers, and $\mu(n)=0$ otherwise. It is classical that for all $a,b\i …