All Questions
10 questions with no upvoted or accepted answers
10
votes
0
answers
373
views
Local Langlands Correspondence for unramified principal series representations
Let $G$ be a connected, reductive group over a $p$-adic field $k$. Assume $G$ is quasi-split with Borel subgroup $B = TU$. Consider those irreducible admissible representations $\pi$ of $G(k)$ which ...
- 6,180
5
votes
0
answers
288
views
Do infinite and ramified local factors of the Dedekind zeta function of a tame number field characterize its local root numbers?
Let say you have two number fields, that are tamely ramified, and suppose that the $p$-part of their Dedekind zeta functions coincide for all prime $p$ which is ramified in either field. Suppose ...
- 2,396
3
votes
0
answers
97
views
Study of relative class number of 'non-abelian' CM field by using L-functions
I'm currently interested in finding good upper bounds for the relative class numbers of non-abelian CM-fields.
So I'm looking for some references to learn the techniques that can be useful.
So far, I ...
- 1,013
3
votes
0
answers
139
views
L-functions for the Weil group over short exact sequences
Let $(\rho,V)$ be a continuous finite dimensional representation of the Weil group $W_F$ over a local field $F$. If $V$ decomposes as a direct sum $V_1 \oplus V_2$ of representations, then
$$L(s,\...
- 6,180
3
votes
0
answers
540
views
Questions about the exceptional zeros of Dirichlet $L$-functions
I have couple questions regarding the exceptional zeros of Dirichlet $L$-functions. We have the following result:
There is a constant $c_1 > 0$ such that $L(\sigma, \chi) \not = 0$ whenever
$$
\...
- 3,625
3
votes
0
answers
163
views
Oscillatory integral moments of $L(\frac{1}{2} + it, f \times f)$
Understanding moments and subconvexity bounds for $L$-functions is a big topic with a lot of activity. I'm currently looking at a related problem, bounding
$$
\int_0^T L\left(\tfrac{1}{2} + it, f \...
- 1,570
2
votes
0
answers
147
views
Well-known estimate for $L(s,\chi)$ for $\sigma=\text{Re}s\geq 1/2$
This is a very short question.
Let $s=\sigma+it$ be a complex number with $\sigma \geq 1/2$.
In the paper 'Jutila, Matti. "On the Mean Value of $L(1/2, \chi)$ FW Real Characters." Analysis 1.2 (...
- 663
2
votes
0
answers
100
views
Function equation over general number fields
Let $\chi$ be a Hecke character on a number field $k$, where could I find a precise reference for the function equation of the $GL(1)$ L-functions
$$L(s, \chi)?$$
I only find references for the case ...
- 927
1
vote
0
answers
131
views
Analytic properties of $L$-functions attached to a compatible system of $\ell$-adic Galois representations
Let $F$ and $E$ be number fields, $G_F$ be the absolute Galois group of $F$, and $S$ be a finite set of primes of $F$. For $\lambda$ a prime of $E$ we denote by $\ell$ its residual characteristic. We ...
- 663
1
vote
0
answers
126
views
Reference request: unfolding of Integral representation of an L-function
Are there any text or papers that thoroughly address unfolding of integral representation of an L-function such as D. Ginzburg's On Spin L-function for Orthogonal Groups page 762-763 and page 774 (or ...
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