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comment Anomalous dimensions in the $O(N)$ model
@Adam I guess Peskin-Schroeder gives the results for $3+1$. Can you kindly give a reference to all the many results that you quoted in your first comment?
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comment Mellin transform between heat kernel and zeta-function
@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?
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comment Mellin transform between heat kernel and zeta-function
@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?
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comment Mellin transform between heat kernel and zeta-function
@shu Isn't the first equality in Liviu's answer the self-adjoint-ness?
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comment Mellin transform between heat kernel and zeta-function
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?
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