Timeline for A unified description of zeta functions of a curve over $\mathbb{F}_q$ and Riemann $\zeta$ function

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Jul 31, 2012 at 5:57	comment	added	Damian Rössler		@Chandan Singh Dalawat. In fact it is $\zeta(s)\zeta(s-1)$, where $\zeta(s)$ is the Riemann zeta function. The point I wanted to make is that zeta functions are defined for varieties over a global field, which is either a number field or the function field of an algebraic curve over a finite field. A simpler example is of course $\bf Q$ itself, which gives the Riemann zeta function, as you say.
Jul 31, 2012 at 3:31	comment	added	Chandan Singh Dalawat		@Damian: of the projective line over $\mathbf{Q}$ ? I had always thought that it was the zeta function of $\mathrm{Spec}(\mathbf{Z})$.
Jul 30, 2012 at 23:15	answer	added	David Hansen		timeline score: 2
Jul 30, 2012 at 23:01	vote	accept	CommunityBot
Jul 30, 2012 at 22:48	answer	added	Qiaochu Yuan		timeline score: 7
Jul 30, 2012 at 22:41	comment	added	Damian Rössler		Have a look at J-P Serre, "Facteurs locaux des fonctions zêta...", Séminaire Delange-Pisot-Poitou, tome 11, no. 2 (1969-1970), exp. 19. (available on NUMDAM). In the setting of Serre, the Riemann zeta function is essentially the zeta function of the projective line over $\bf Q$.
Jul 30, 2012 at 22:19	history	asked	user16974	CC BY-SA 3.0