Timeline for Zeros of inverse of dilogarithm
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 12, 2022 at 10:25 | comment | added | Tom Goodwillie | @DrorSpeiser : If it's true then I think you can find it in arxiv.org/abs/alg-geom/9202022 (section 2, Monodromy). | |
| Oct 12, 2022 at 7:51 | comment | added | Dror Speiser | @HenriCohen : nah, try increasing truncation degree and you'll see that zero disappear | |
| Oct 12, 2022 at 6:49 | comment | added | Dror Speiser | @TomGoodwillie : that's what I would hope for. Can this be proved? | |
| Oct 12, 2022 at 6:47 | comment | added | Dror Speiser | @Conrad : the compositional inverse can be defined from the power series, and I don't think it's a multivalued function. This is similar to log being multivalued but exp is not. | |
| Oct 12, 2022 at 1:04 | comment | added | Tom Goodwillie | That is, the numbers that arise as values of the multi-valued function $Li_2(x)$ at $x=0$ are precisely the numbewrs $4\pi^2k$, $k\in\mathbb Z$. | |
| Oct 12, 2022 at 1:03 | comment | added | Tom Goodwillie | I think that the answer is: the integer multiples of $4\pi^2$. | |
| Oct 12, 2022 at 0:03 | comment | added | Conrad | what do you mean by compositional inverse and also by $Li_2$ (in the sense that $Li_2$ is a multivalued function with branch points at $1, \infty$ so do you think of $Li_2$ as defined on say the complex plane minus $[1,\infty]$ as the "main branch" or something else? | |
| Oct 11, 2022 at 20:47 | comment | added | Martin Rubey | I have no idea whether it helps, but it is at least fun - the compositional inverse satisfies a relatively nice differential equation: $x^{3} f'\left(x\right)^{3} + {\left(x + 1\right)} f\left(x\right)^{3} + 3 \, x f\left(x\right)^{2} f'\left(x\right) - {\left(x^{2} - {\left(x^{3} + 3 \, x^{2}\right)} f\left(x\right)\right)} f'\left(x\right)^{2} - f\left(x\right)^{2} - {\left(x^{3} f\left(x\right)^{2} - x^{2} f\left(x\right)\right)} f''\left(x\right) = 0$ | |
| Oct 11, 2022 at 20:24 | history | edited | Ira Gessel | CC BY-SA 4.0 |
deleted 1 character in body
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| Oct 11, 2022 at 19:57 | history | asked | Dror Speiser | CC BY-SA 4.0 |