Weil conjectures 1 Introduction

This talk is the first of a series of talks on the Weil conejctures.
We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varieties of
higher dimension over finite fields, and conclude by stating the Weil conjectures about these zeta functions, including the analog of the Riemann hypothesis.

[jeparlefrancais]

It's such a blessing you making these videos.

[theflaggeddragon]

What a fabulous birthday present! Thank you for these wonderful videos Professor Borcherds.

[MrMaddeen]

Prof, thank you so much for making this video.

[hausdorffm]

What is the definition of N(D) at 6:32?

13:10 The number of divisors equals to q^d. This is because, each ideal corresponds to some irreducible polynomial f = x^d+c_{d-1}x^{n-1} + .... + c_0 and the all polynomial of such f corresponds to all pairs of coefficients (c_0, c_1, ..., c_{d-1}) in k^n. Because q is the cardinality of k, the number of possible pairs (c_0, c_1, ..., c_{d-1}) is q^d. But I cannot understand how to deal the irreducibility of f by the coefficients? I guess, the count q^d drops the irreducibility of f. Probably I misunderstand :'-D
Each p_i corresponds to a irreducible polynomial. So, the sum of n_ip_i corresponds to polynomial which is not necessarily irreducible?

[k-theory]

When he's talking about "compactifying specZ", is he reffering to F1-geometry?

[truthteller]

Hello, Mr Borcherds. Thankyou for making these videos. You are a great mathematician. It would be even better if you got some good lighting on the left hand side and got a good frame rate.

[truthteller]

Hello Professor. How did you prove the Monstrous Moonshine Conjecture? In fact, how do you even define the Monster Group at all?