Proof Of The Collatz Conjecture

When Vera heard Lu Zhou's praise, she smiled brightly.

This was undoubtedly the best compliment she had ever been given.

As she stood next to Lu Zhou, she said in a low voice, "Your guess is correct, Collatz conjecture is a number theory problem. It's also a complex analysis problem…"

In as early as 1994, L.Berg and G.Meinardus proved that the 3n+1 conjecture was equivalent to the function equation h(z3) = h(z^6)+{h(z2)+λh(λz2)+λ2h(λ2z2)}/3z (where λ=e^(2πi/3)). This could be expressed through the unit disc {z:|z|<1} as h(z) (where h0 and h2 are complex constants).< p>

In 1998, D.Schliecher used this foundation to prove that any integral function in the form of h(z) results in g(z) = z/2 + (1-cos(πz)(z+1/2)/2+1/π(1/2-cos(πz)sin(πz)+h(z)sin^2(πz)).