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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

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What is the lattice point distribution over binary quadratic forms?

Let $f(x,y)=x^2+ny^2$ be the binary quadratic form of interest and consider the lattice points $S=\{ (x,y,f(x,y)) \in \mathbb{N}^3 \}$. For simplicity, we keep things only on quadrant I of the Cartesi …