Timeline for Vanishing of certain periodic series: A question related to $L(1 , \chi) \neq 0$.
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2015 at 14:47 | vote | accept | George Shakan | ||
| Jan 25, 2015 at 6:06 | comment | added | Noam D. Elkies | Thanks. Basically I just used the routine lindep in gp. Once one has guessed such an identity numerically it's usually not hard to prove. Here $f(n)$ is odd and 7-antiperiodic, so $\sum_{n=1}^\infty f(n)/n = 0$ comes down to a linear relation among the cosecants of multiples of $\pi/7$, namely $$ \frac1{\sin \pi/7} = \frac1{\sin 2\pi/7} + \frac1{\sin 3\pi/7}. $$ | |
| Jan 24, 2015 at 22:25 | comment | added | George Shakan | Very cool..would you mind elaborating a little bit on how you found this? | |
| Jan 24, 2015 at 20:45 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |