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visits member for 4 years, 1 month
seen Sep 25 at 13:24

Marc Palm

Postdoc in Mathematics

http://www.plusepsilon.de


Sep
19
comment Are there any simple, interesting consequences to motivate the local Langlands correspondence?
@PaulSiegel: I have edited the question. I was probably thinking "global understanding requires local understanding". That is not necessarily so, I guess.
Jun
30
comment Eisenstein series over a definite division algebra
Ah okay, I see my mistake. I was thinking $GL(1)$ over a division algebra, you are considering $GL(2)$. Moeglin-Waldspurger do not consider this setting in their book?
Jun
27
comment Eisenstein series over a definite division algebra
Please help me to understand what the cusp is. I recall that quaternion division algebras give rise to compact quotients, hence no cusps and Eisenstein series. The trace formula becomes simple and one gets the Jacquet-Langlands correspondence with forms with at least two square-integrable components.
Jun
19
comment Complex zeros of $\zeta'(s)/\zeta(s) + \zeta'(1-s)/\zeta(1-s) $ = simpler expression (except at zeta zeros)
How do cancel the Euler products? Seems like you only got the $\Gamma$ factor.
Jun
19
comment Complex zeros of $\zeta'(s)/\zeta(s) + \zeta'(1-s)/\zeta(1-s) $ = simpler expression (except at zeta zeros)
$\xi(s) = \xi(1-s)$, isn't it? What is your definition of $\xi$?
Jun
14
comment Are there any simple, interesting consequences to motivate the local Langlands correspondence?
Is there a local version of the Taniyama-Shimura conjecture? Also it proves the Ramanujan conjecture in the global setting, but this does not apply to the local steting at all, where actually non-tempered things play a role.
Jun
11
comment Analytic criteria for the support of the Plancherel measure for SL(2,Qp), spherical functions
Characteristic functions are not smooth. Growth considerations are pretty analytic to me. For any thing else, there are not that many analytic differences between the characters. It's like $x \mapsto e^{sx}$ for $s$ varying and $s$ being imaginary means temperedness.
Jun
10
comment Spherical functions for sl(2,Q_p)
I gave the formula for the distribution. It is general. If you want to find a function on $G$ corresponding to this, I can't tell where to look for explicit computations. My feeling is that finding some useful computational analogy can only done to some extent. $P$-adic Gamma factors do not look like real or complex Gamma-functions.
Jun
10
comment Spherical functions for sl(2,Q_p)
Being in the left regular correspond to being tempered, so you will not get the trivial representation nor the non-tempered principal series. But it does not matter, my computation assume $\mu$ general, not necessarily unitary. You probably means character seen as a function, which is locally integrable - not as a distribution. Yes you can do a similiar things whether as long as you assume admissible.
Jun
2
comment Spherical functions for sl(2,Q_p)
Being type I and having spherical functions are different things. Please clarify your question.
May
20
comment surjective homomorphism with compact kernel (Milne's note on Shimura varieties)
Please define the notation.
May
20
comment Fourier series of functions on compact groups
If you use the framework of Hilbert's 5th problem, you can generalize it to the locally compact version, see chapter 6 of my Phd Thesis.
May
20
comment Fourier series of functions on compact groups
Harish-Chandra (1966), "Discrete series for semisimple Lie groups. II. Explicit determination of the characters",
May
13
comment Decomposition of $L^2(\Gamma \backslash G)$
Multiplicity one is known not to hold for SL(n), so no simplicity of the eigenvalues. It is a reasonable conjecture to assume that given a lattice, the multiplicity is bounded by a constant depending on the lattice and the weights.
May
12
comment Constant terms of Eisenstein series and Gindikin-Karpelevich formula
Did you check Moeglin-Waldspurger's book on Eisenstein series?
Apr
30
comment Has universality been definitely established for the whole Selberg class?
authors... I d send a joint email at all of them in this case.
Apr
30
comment Has universality been definitely established for the whole Selberg class?
Did you ask the author via email?
Apr
30
comment Has universality been definitely established for the whole Selberg class?
Please add references.
Apr
30
comment Current Status on Langlands Program
@Emerton: I thought that stabilization solves the issue that distinct conjugacy classen in $G(F)$ become conjugated in $G(\overline{F})$. This does not seem to happen for $GL(n)$, hence I thought the trace formula on $GL(n)$ is stable by definition. That's all what I meant to say.
Apr
17
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 $p$.