### M Theory Lesson 193

While I was busy at Neutrino 08, the NCG blog posted an update on the Vanderbilt meeting. In particular, they note that Manin's lectures on Zeta functions and Motives are available at Katia Consani's homepage! Niranjan Ramachandran spoke about this paper at Vanderbilt. This work, originating in the physical ideas of Deninger, looks at the field over one element (which is fast becoming a popular subject). Deninger writes the zeta function, completed with the infinite prime, in the form

$\zeta (s) = \frac{R}{s (s - 1)}$

where $R$ is a regularized determinant to be viewed as an infinite dimensional analogue of a determinant of an endomorphism of a finite dimensional vector space (according to Connes and Consani).

$\zeta (s) = \frac{R}{s (s - 1)}$

where $R$ is a regularized determinant to be viewed as an infinite dimensional analogue of a determinant of an endomorphism of a finite dimensional vector space (according to Connes and Consani).

## 5 Comments:

Kea

Have you taken a look at the MIT OpenCourseWare notes on fat graphs, Euler characteristics of moduli spaces and Matrix integrals?

Dear Kea,

have you idea what this completion with infinite prime(s?) means in this context?

Matti, look at the Deninger papers. It is explained at the start.

That's pretty cool, kneemo, but it wasn't clear to me where in the notes they talk about ribbon graphs. I didn't feel like wading through them, but thanks for the link!

Oh, browse the notes for Chapter 4: Matrix Integrals, section 4.1 covers fat graphs.

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