Timeline for Mellin transform between heat kernel and zeta-function
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2013 at 13:37 | comment | added | Student | @LiviuNicolaescu Can you give a reference to these kind of representations also? So you are saying that these two kinds of integral representations of the zeta function are unrelated? | |
| Aug 22, 2013 at 8:11 | comment | added | Liviu Nicolaescu | That integral description of zeta is not that subtle. | |
| Aug 21, 2013 at 21:57 | comment | added | Student | @Liviu Thanks for the reference! Will read that. On a related note I was wondering if this integral representation of the generalized zeta-function related to these kinds of identities like, $\xi(3) = \frac{8\pi^3}{3}\int_0^{\infty}d\lambda \frac{\sqrt{\lambda}}{1+e^{2\pi\sqrt{\lambda}}}$ - could you kindly shed some light? | |
| Aug 21, 2013 at 14:06 | comment | added | Liviu Nicolaescu | On noncompact manifolds there is a first issue namely the selfadjointness of $D$. If $M$ is a complete manifold, and $D$ is the usual Laplacian, then it has a unique selfadjoint extension to $L^2$. For complete hyperbolic manifolds check this paper and the references therein. archive.numdam.org/ARCHIVE/JEDP/JEDP_1987___/JEDP_1987____A17_0/… | |
| Aug 21, 2013 at 13:45 | comment | added | shu | @Anirbit, Last identity is almost the definition of Gamma function by changing the variable $t\to \lambda t$. | |
| Aug 21, 2013 at 13:25 | vote | accept | Student | ||
| Aug 21, 2013 at 13:24 | comment | added | Student | Nicolescu Thanks for your efforts. (1) I am not sure I find the last identity "elementary" ;P - I was infact stuck on that before I posted this question! (2) Can you comment on what happens on hyperbolic manifolds? Anything (what if?) changes in the argument of yours? | |
| Aug 20, 2013 at 19:12 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
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| Aug 20, 2013 at 17:18 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
added 7 characters in body
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| Aug 20, 2013 at 15:43 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |