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Marc Palm

Postdoc in Mathematics

http://www.plusepsilon.de


2h
comment Can $T$ act trivial in a repn of SL$_2(\mathbb{Z}_N)$?
Proof seems right, although hard to read: I'd have rather writen
1d
comment Can $T$ act trivial in a repn of SL$_2(\mathbb{Z}_N)$?
Be careful that $p$ is much easier than $p^k$. I actually don't understand your proof even for the case $p$.
1d
comment Phillips-Sarnak conjecture in higher dimension
What about superrigidity? Does it not contradict your claim about existence of non-arithmetic lattices in higher rank? en.wikipedia.org/wiki/Superrigidity
1d
comment Are the only discrete groups with nontrivial p-adic Haar measure finite?
What is a tight measure? How is the isometry between $M(G)$ and $c_0(G)$? Usually $c_0(G)' = M(G)$, so there is a dual. I can't actually see why it should matter $C_p$ or $C$ valued measures here. It is more likely to see where you go wrong if you add all definitions.
Apr
14
comment The sum over zeros in the explicit formula for $\zeta(s)$
If you mean the explicit formula of Weil, the test function should be bounded by $(1+|\im z|))^{2 + \epsilon}$ and we also have absolute convergence there. So I am not sure if your argument can be made rigorous, because it would imply an explicit formula with more relaxed conditions on the allowed test functions.
Apr
12
comment What is the current status of representations of $GL_n(F)$ (and other algebraic groups)?
I also recommend Bushnell-Henniart Local Langlands for GL(2) for the Bushnell-Kutzko theory. It is more digestible for a beginner, I think.
Apr
11
comment What is the current status of representations of $GL_n(F)$ (and other algebraic groups)?
Thanks, that's what I meant.
Apr
11
comment What is the current status of representations of $GL_n(F)$ (and other algebraic groups)?
When $F$ is local non-archimedean field,...
Apr
11
comment What is the intuition behind the definition of cuspidal representations?
"some and therefore every"
Apr
10
comment What is the intuition behind the definition of cuspidal representations?
Yes the unipotent radiacal of any Borel subgroup (defined over $F$). Note that your are allowed to conjugate by elements of $GL_2(F)$. There are may expositions on how to move between classical and adelic language, see e.g. Bump's book.
Apr
10
comment leading-order behaviour of riemann zeta function?
$\zeta$ gets arbitrary small in $1/2 \leq \Re s <1$. I am not sure about $0< \Re s <1/2$.
Apr
10
comment leading-order behaviour of riemann zeta function?
I am not getting it? Is your "I'm looking for something...." not stronger then LH, which is certainly not known?
Apr
10
comment Reference for Kronecker-Weyl theorem in full generality
Sorry, I didn't see the part: " a proof under the assumption that the θj are linearly independent over the rational numbers will not suffice for me." I deleted my answer.
Apr
8
comment Inequality for a gamma function
The logarithmic derivative of the Selberg Zeta function grows like $CT^2$ as $\Im z = T \rightarrow \infty$, which can be seen from the Weyl law. More important for its growth is the Barnes-G-function. $\Gamma$ contributes at most $T \log(T)$ in the non-compact setting.
Apr
8
comment Characters and conjugacy classes
For infinite groups unitary irreducible representations seperate points: Gelfand-Raikov theorem
Apr
7
comment What is the logarithmic derivative of an (intertwining) operator?
Note that my computation apply only to the highest type. For the computations at the real places and the unramified complex cases, you can have a look at my PhD thesis. There is a good reason for working with highest types/smallest weights = irreducible $K$-reps as soon as you have pinned down the local conditions.
Apr
6
comment Homeomorphisms that admit a decomposition
Okay, my mistake;) I see now that it seems to more complicated...
Apr
5
comment Homeomorphisms that admit a decomposition
There are only two strictly monotone functions on $[0,1]$ up to conjugation by homeomorphisms. One doesn meet your criteria.
Apr
5
comment Homeomorphisms that admit a decomposition
Do you know the answer for $[0,1]$? Modulo conjugating by homeomoprhism of $[0,1]$, there seems to be only one map.
Apr
5
comment Space with 720° / not 2$\pi$ rotational symmetry?
Perhaps the Möbiusband?