# Tagged Questions

Questions about Selberg class and the related conjectures such as the analogue of Riemann Hypothesis, Selberg's orthonormality conjecture, degree conjecture, general converse conjecture that says the Selberg class exactly consists of automorphic L-functions, etc.

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### Assymptotics of a Selberg type integral

Does any one know some references/ ideas on how to study the assymptotics as $N$ goes to $\infty$ of the following Selberg type integral \int _{\mathbb R^N} e^{-|x|^2}\ \prod_{1\le i<j\le N} \...
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### Galois classes of L-functions

Around one month ago, I posted on math.stackexchange a draft I wrote in which I define the notion of Galois class of L-functions: see http://math.stackexchange.com/questions/280876/definition-of-a-...
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### Strong automorphisms of the Selberg class

Following Automorphisms of the Selberg class, I define strong automorphisms of the Selberg class by adding as an hypothesis that every invariant of $F$ (i.e all the $H$-invariants, conductor and root ...
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### Automorphisms of $\mathbb{C}$, Selberg class and surjectivity

Let $F$ be an element of the Selberg class and $\sigma$ be a field automorphism of $\mathbb{C}$ such that $\sigma\circ F=F\circ\sigma$. Let $Fix_{\sigma}$ be the set of all complex numbers $z$ such ...
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### A possible application of representation theory to Galois classes of L-functions

I define the notion of a Galois class of L-function as follows: $A$ is a Galois class of L-functions if and only if the following conditions simultaneously hold true: 1) $A$ is a subset of the ...
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### Is a certain group related to a primitive L function isomorphic to $Gal(\overline{\mathbb{Q}}_{\ell}/\mathbb{Q}_{\ell})$ for some $\ell$?

I define the notion of "Galois class of L functions" in the following way: $A$ is a Galois class of L functions if and only if the follwing three conditions hold simultaneously: 1) every element ...
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### Automorphisms of S and representations

EDIT July 22nd 2013: I add further details in bolded sentences: Assuming Selberg's orthonormality conjecture and following Automorphisms of the Selberg class, I define automorphisms of the Selberg ...
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### Would countability conjecture and degree conjecture imply unique factorization for the Selberg class?

I already asked this question on MSE but didn't get any comment or answer, so I ask it here. Assuming countability conjecture as stated in http://www.mat.unimi.it/users/molteni/research/papers-pdf/4-...
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### Would a proof of both (G)RH and Montgomery's pair correlation conjecture imply SOC?

Would a proof of both (G)RH and Montgomery's pair correlation conjecture imply SOC? It seems, judging by the abstract of a 2002 paper of Ram Murty and a possibly Romanian co-author published on www....