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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 …
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 …
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 …