Timeline for How can I transform $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n^k\sin(\pi rn)}$ into a modular form?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 22, 2023 at 21:39 | vote | accept | Milo Moses | ||
| Jan 30, 2021 at 5:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 8, 2021 at 20:20 | comment | added | Marcus | Also very similar, though not exactly the same: Have a look at Ramanujan's Notebooks - Part II (by Berndt), Chapter 14 on Infinite Series, Formula 1.14 (p. 245 on top) | |
| Jan 1, 2021 at 9:05 | comment | added | Marcus | I haven’t checked that, but it’s in the same vein. For a link to Eisenstein series, see arminstraub.com/downloads/pub/ramanujanzeta.pdf | |
| Dec 31, 2020 at 17:48 | comment | added | Milo Moses | @Marcus The main theory in the linked paper seems to be of relation functions similar to $f_k(z)$ back to themselves using the theory of differential equations, and so if I am not mistaken my result does not follow from theirs and theirs does not follow from mine. Is that correct? | |
| Dec 31, 2020 at 17:40 | comment | added | Milo Moses | @Marcus This is so funny! When I started researching and proved the main identity, the first thing I did was prove results about $f_k(\rho)$ being a rational times $\pi^k$ when $\rho$ is a quadratic irrational. It is such a small world! | |
| Dec 31, 2020 at 9:07 | comment | added | Marcus | Have a look at Armin Straub's work, e.g., "Special values of trigonometric Dirichlet series and Eichler integrals" (arxiv.org/abs/1407.5119 - in particular page 5) | |
| Dec 30, 2020 at 21:11 | history | edited | Milo Moses | CC BY-SA 4.0 |
added 2 characters in body
|
| Dec 30, 2020 at 18:36 | answer | added | Milo Moses | timeline score: 4 | |
| Dec 30, 2020 at 0:15 | history | edited | Milo Moses | CC BY-SA 4.0 |
deleted 5 characters in body
|
| Dec 29, 2020 at 23:23 | history | asked | Milo Moses | CC BY-SA 4.0 |