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508 views

### 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 ...

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219 views

### Automorphisms of the L-function associated to an elliptic $\mathbb{Q}$-curve

Edited after Noam Elkies' comment: From what I understand (very few actually), there exist elliptic curves defined over some number fields $\mathbb{K}$ Galois over $\mathbb{Q}$ which are isogenous to ...

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131 views

### 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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26 views

### 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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34 views

### 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 ...

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368 views

### 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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152 views

### 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 ...

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110 views

### 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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267 views

### 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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109 views

### Invariants of an L-function

For any element $F$ of the Selberg class, one can define invariants of $F$ such as the degree, the conductor, the h- invariants, etc. My question is: these any known set of invariants such that a ...

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55 views

### Order of non-trivial zeros of an L-function and topological dimension

Let $F$ be a primitive element of the Selberg class of degree $d_{F}>0$, and let's consider the group $G$ of complex isometries of finite order that preserve the critical strip ...

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197 views

### Automorphisms of an L-function

Throughout this question, the term "L-function" will denote any element of the Selberg class. Following Strong automorphisms of the Selberg class, I define the group of automorphisms of an L-function ...

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97 views

### Are the d quantities log Gamma(\lambda_j.s+\mu_j) linearly independent over Q for all s>1?

This question deals with the gamma factor of a primitive function of the Selberg class. Writing the functional equation of such a function $F$ as $\Phi(s)=\overline{\Phi(\overline{1-s})}$ with ...

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103 views

### Selberg's orthonormality conjecture and permutations

Let $(F_n)_{n>0}$ be an enumeration of the primitive elements of the Selberg class. Let $F_i$ and $F_j$ be such primitive L-functions. What is known about the group $G(i,j)$ of permutations ...