3. Another section
testing x^x foo bar-
Let c(h/k):=V(\overline{h},k).
Problem 3.05.
[Brian Conrey] Prove that c satisfies a reciprocity formula \begin{eqnarray} xc(x)+c(1/x)-\frac{1}{\mbox{Den}(x)}=\psi(x) \end{eqnarray}where \psi(x) can be analytically continued to \mathbf{C}', the complex plane minus the negative real axis.-
Remark. What does "Den" mean?
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This is a complicated equation
Problem 3.15.
\begin{eqnarray*} \sum_{n=1}^\infty \frac{1}{n^2}&=& 1+\frac{1}{2^2}+\frac{1}{3^2}+\dots \\ &=& \frac{\pi^2}{6}. \end{eqnarray*} -
The Four Color theorem
This is a famous old problem.Conjecture 3.2.
[Rob Beezer] A planar map can be colored with four or fewer colors and there is a proof without a laborious number of cases.-
Remark. Test remark
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Remark. 33
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Remark. [aaa] Something new.
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Remark. testo
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Recall that the Vasyunin sum is V(h,k)=\sum_{a=1}^{k-1}\frac{a}{k} \cot \frac{\pi \overline{a} h}{k}.
Problem 3.45.
[Brian] Prove that V(-h,k)=V(h,k).
Cite this as: AimPL: Try out this list!, available at http://aimpl.org/test.