# 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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### Non-vanishing of L-values for twists of Hilbert modular forms

Let $F$ be a real quadratic field, and let $f$ be a Hilbert modular form over $F$ of parallel weight 2. It's known, by a theorem of Rohrlich, that there exist infinitely many Hecke characters of $F$ ...
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### Functional derivatives on Banach spaces

Physicists often use functional integrals and I'm trying to make sense of it in more precise terms. As you can see here, the functional derivative in Physics is defined in terms of Taylor expansions. ...
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### Is an automorphic form of $\operatorname{GL}_{n}(\mathbb{A}_{\mathbb{Q}})$ determined by its L-function?

To an automorphic representation $\pi$ of $\operatorname{GL}_{n}(\mathbb{A}_{\mathbb{Q}})$ one can associate its L-function $s\mapsto L_{\pi}(s)$. Is the map $\pi\mapsto L_{\pi}$ bijective?
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### Sets of L-functions being “almost bimonoids”

Let $\mathcal{M}$ be a set of L-functions (where by L-function I mean any L-function associated to an automorphic representation of $\operatorname{GL}_{n}(\mathbb{A}_{\mathbb{Q}})$ which is an element ...
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### Relations between spectral parameters of automorphic representations

Let $\pi$ be an automorphic representation (say, trivial central character) of $GL(2)$. Let $\alpha(p)$ and $\beta(p)$ denote its spectral parameters at the place $p$, that is to say the associated ...
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