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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

8 votes
2 answers
464 views

Regularity assumption in the simple trace formula

In the simple trace formula of Deligne Kazhdan one assumes that the test function is supported at the elliptic regular elements at one place and is a supercusp form at another place. Why can't one ju …
jaycegetz's user avatar
  • 412
4 votes
1 answer
719 views

Reference for: Every local field can be realized as the completion of a global field

It is well known that every local field (i.e. nondiscrete topological field locally compact with respect to the topology) is the completion of some global field. I know the argument, a nice expositio …
jaycegetz's user avatar
  • 412
9 votes

What is the Twisted Trace Formula?

For simplicity assume that $G$ is a reductive $\mathbb{Q}$-group that is anisotropic. Assume that it admits an automorphism $\theta$. Let $f \in C_c^\infty(G(\mathbb{A}))$. One has the usual kernel …
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  • 412