# Questions tagged [l-functions]

Questions about generalizations of the Riemann Zeta function of arithmetic interest whose definition relies on meromorphic continuation of special kinds of Dirichlet series, such as Dirichlet L-functions, Artin L-functions, elements of the Selberg class, automorphic L-functions, Shimizu L-functions, p-adic L-functions, etc.

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### The link between Satake parameter and Godement-Jacquet L-function of an automorphic representation of $GL_{n}$

Origin of the question: I'm reading the following survey of K. Martin, more generally I'm looking for the "best way" to define L-function associated to an automorphic representation of a ...
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### Does any element of an L-rig fulfill Rudnick and Sarnak hypothesis H and thus Selberg orthogonality conjecture?

I introduce the notion of L-rig in the first paragraph of Are there infinitely many L-rigs? Calling "genuine L-function" any element of an L-rig, and to the light of recent results about L-...
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### Is $\frac{1}{L(1+it)}$ unbounded?

Let $\chi$ be a Dirichlet character and $L(s, \chi)$ be the corresponding L-function. Is $$\frac{1}{L(1+it, \chi)}$$ unbounded for $t \in \mathbb{R}$? I'm aware that this is true if $L=\zeta$, but I'm ...
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### Do Artin L functions have polynomial growth in in the critical strip?

Given an irreducible representation $\rho$ of the Galois group $G$ of a number field $K$ over $\mathbb{Q}$, we have the associated Artin $L$ function which we denote by $L(s, \rho)$. By Brauer ...
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### Explanation about Lapid-Rallis iductive argument (doubling method)

I am reading Lapid-Rallis "On the local factors of representations of classical groups" and I am completely stuck with the proof of Proposition 3. In the case $\mathcal V$ is not anisotropic,...
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### Have there been recent developments of Booker's approach to L-functions as distributions?

Andrew Booker introduced a framework to study L-functions through distributions in https://arxiv.org/abs/1308.3067v2. This allowed him and others to get new results about zeros of automorphic L-...
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### The Guinand-Weil explicit formula for Hecke characters

The Guinand-Weil formula for the Riemann zeta function is \begin{aligned}&\Phi (1)+\Phi (0)-\sum _{\rho }\Phi (\rho )\\={}&\sum _{p,m}{\frac {\log(p)}{p^{m/2}}}{\Big (}F(\log(p^{m}))+F(-\log(p^...
1 vote
I'm trying to compute special values of Hecke L-function for the field $K=\mathbb{Q}(\sqrt{1})$ using Magma (more exactly, I need $L(k, \chi^k)$, $k$ - integer, $\chi$ - Hecke character for the ...