Timeline for Does this multiplicative function have a name? If so, what is known about it?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2018 at 15:03 | comment | added | Peter Humphries | @GHfromMO, yep, which is why it comes up in the field automorphic forms so often! | |
| Oct 18, 2018 at 14:36 | comment | added | GH from MO | @PeterHumphries: Indeed the function looked familiar! It is also the index of $\Gamma_0(n)$ in $\Gamma_0(1)$ if I am not mistaken. | |
| Oct 18, 2018 at 14:35 | comment | added | GH from MO | @MartinSleziak: Thanks for your comment. Clearly, one can also prove this statement by elementary means, by making use of the convolution I mentioned. | |
| Oct 18, 2018 at 14:07 | comment | added | Peter Humphries | In the field of automorphic forms, this function is often denotes $\nu(n)$ (for example, in Iwaniec-Luo-Sarnak's seminal paper on low-lying zeroes of $L$-functions of holomorphic cuspidal eigenforms). | |
| Oct 18, 2018 at 13:58 | comment | added | Martin Sleziak | I will just add this function appears in Exercise 11 in Chapter 3 in Apostol's book. The last part of this exercise is the asymptotic formula $\sum_{n\le x} \varphi_1(n)=\frac{\zeta(2)}{2\zeta(4)}x^2+O(x\log x)$. (Apostol denotes the function by $\varphi_1$.) | |
| Oct 18, 2018 at 13:58 | history | edited | GH from MO | CC BY-SA 4.0 |
added 15 characters in body
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| Oct 18, 2018 at 13:53 | vote | accept | Stanley Yao Xiao | ||
| Oct 18, 2018 at 13:50 | history | answered | GH from MO | CC BY-SA 4.0 |