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pro vyhledávání: '"Solomatin, Pavel"'
Autor:
Solomatin, Pavel
In this short note we provide a few examples of non-isomorphic arithmetically equivalent global function fields. These examples are obtained via well-known technique of adjoining the torsion points of various Drinfeld Modules to realise the $Gl_n(\ma
Externí odkaz:
http://arxiv.org/abs/2107.08250
Autor:
Solomatin, Pavel
Given a number field $K$ one associates to it the set $\Lambda_K$ of Dedekind zeta-functions of finite abelian extensions of $K$. In this short note we present a proof of the following Theorem: for any number field $K$ the set $\Lambda_K$ determines
Externí odkaz:
http://arxiv.org/abs/1901.09243
Autor:
de Smit, Bart, Solomatin, Pavel
The main purpose of this paper is to extend results on isomorphism types of the abelianized absolute Galois group $\mathcal G_K^{ab}$, where $K$ denotes imaginary quadratic field. In particular, we will show that if the class number $h_K$ of an imagi
Externí odkaz:
http://arxiv.org/abs/1703.07241
Autor:
de Smit, Bart, Solomatin, Pavel
The main purpose of this paper is to describe the abelian part $\mathcal G^{ab}_{K}$ of the absolute Galois group of a global function field $K$ as pro-finite group. We will show that the characteristic $p$ of $K$ and the non $p$-part of the class gr
Externí odkaz:
http://arxiv.org/abs/1703.05729
Autor:
Solomatin, Pavel
In this paper we present an approach to study arithmetical properties of global function fields by working with Artin L-functions. In particular we recall and then extend a criteria of two function fields to be arithmetically equivalent in terms of A
Externí odkaz:
http://arxiv.org/abs/1610.05600
Autor:
Solomatin, Pavel
Initially motivated by the relations between Anabelian Geometry and Artin's L-functions of the associated Galois-representations, here we study the list of zeta-functions of genus two abelian coverings of elliptic curves over finite fields. Our goal
Externí odkaz:
http://arxiv.org/abs/1601.05941
Autor:
Solomatin, Pavel
The problem of constructing curves with many points over finite fields has received considerable attention in the recent years. Using the class field theory approach, we construct new examples of curves ameliorating some of the known bounds. More pre
Externí odkaz:
http://arxiv.org/abs/1508.00267