draks ...
Reputation
11,291
Next privilege 15,000 Rep.
Protect questions
 1h comment Help to solve $\displaystyle \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty} \frac{\zeta(2s)\zeta(s-1)}{\zeta(2s-2)} \frac{x^{s}}{s} dz$ @user8268 Can't it be done explicitely? 1h revised Help to solve $\displaystyle \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty} \frac{\zeta(2s)\zeta(s-1)}{\zeta(2s-2)} \frac{x^{s}}{s} dz$ edited body 2h asked Help to solve $\displaystyle \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty} \frac{\zeta(2s)\zeta(s-1)}{\zeta(2s-2)} \frac{x^{s}}{s} dz$ 2h comment How to use an inverse Mellin transform to get to the $\mathrm{core}(n)$? @user1952009, ah right, misread Perrons formula. I've read a bit on contour integrals in Edward's book on Riemann's Zeta Function. Why is $c>2$? 2h accepted What is known about these arithmetical functions? 2h asked Use Gröbner bases to count the 3-edge colorings of planar cubic graphs… 2h awarded Notable Question 7h comment How to use an inverse Mellin transform to get to the $\mathrm{core}(n)$? @user1952009: So it boils down to the following: Given $\frac{\zeta(2s)\zeta(s-1)}{\zeta(2s-2)}=\sum_{n=1}^{\infty} \frac{\mathrm{core}(n)}{n^{s}}$ I have to calculate $\displaystyle \mathrm{core}(x) =\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty} \frac{\zeta(2z)\zeta(z-1)}{\zeta(2z-2)} \frac{x^{z}}{z} dz$, correct? 15h revised How to use an inverse Mellin transform to get to the $\mathrm{core}(n)$? added 56 characters in body; edited title 15h revised How to use an inverse Mellin transform to get to the $\mathrm{core}(n)$? deleted 4 characters in body 15h reviewed Leave Open Show that $\langle\cdot,\cdot\rangle : E \times E \to \mathbb{R}$ is a continuous function 15h reviewed Leave Open What are the $GL_n(F)$-orbits of a group action on the set of idempotent matrices? 15h revised Is there matrix representation of the line graph operator? added 4 characters in body 1d comment On groups with presentations $\langle a,b,c|a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=(abc)^s=1\rangle$… My confusion about my substitution... 1d comment On groups with presentations $\langle a,b,c|a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=(abc)^s=1\rangle$… Hey Derek, do you think you can help me? Feb 7 revised How to number the left-hand turn paths of planar bicubic graphs? edited tags Feb 6 comment How to number the left-hand turn paths of planar bicubic graphs? @SashaKolpakov yes, how many path for a given coloring / orientation. Is my proposed way correct? I think your worries are no problem for planar graphs... Feb 5 comment How to number the left-hand turn paths of planar bicubic graphs? @SashaKolpakov I restrict to planar cubic ones where a 3-edge coloring is guaranteed by the 4-color theorem. An orientation can be chosen without respect to the edge coloring, e.g. All orientations can be left (or + as in my other post... Feb 4 comment How to find all proper colorings (four coloring) of a graph with a brute force algorithm +1 interesting... Feb 4 revised How to find all proper colorings (four coloring) of a graph with a brute force algorithm deleted 3 characters in body