2
votes
3answers
211 views

A question on Haar measure on local field.

Let $F$ be a local field of characteristic 0, and $f:F\rightarrow \mathbb{C}$ be an integrable function. Is the following formulation valid? $ \int_{F^\times}f(x^2) d^\times x=\int_{F^{\times 2}}f(x) ...
2
votes
0answers
294 views

Haar measure on Galois groups

Galois groups are nice compact Hausdorff groups, and therefore possess a bounded Haar measure, unique if we insist that the total volume be $1$. What is the Haar measure on the absolute Galois group ...
17
votes
2answers
984 views

The Riemann zeta function and Haar measure on the profinite integers

In an answer to a question on MU about the Riemann zeta function, I sketched a proof that the probability distribution on $\mathbb{N}$ which assigns $n$ the probability $$\frac{ \frac{1}{n^s} ...