# Pavel SolomatinLeiden University | LEI · Mathematical Institute

Pavel Solomatin

Doctor of Philosophy

## About

8

Publications

370

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12

Citations

Citations since 2017

Introduction

I am a Software Developer with PhD in number theory received from Leiden University(2021). For more information: psolomatin.com

Additional affiliations

October 2014 - October 2017

## Publications

Publications (8)

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 $Gl_n(\mathbb F_q)$ as a Galois group of extensions of global function fields. Furthermore we afford the code...

Artin L-functions associated to continuous representations of the absolute Galois group G_K of a global field K capture a lot of information about G_K as well as arithmetic properties of K. In the first part of the present thesis we develop basic aspects of this framework, starting from the well-known theory of arithmetically equivalent number fiel...

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 the isomorphism class of $K$. This means that if for any number field $K'$ the two sets $\Lambda_K$...

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 imaginary quadratic field $K$ different from $\mathbb Q(i)$, $\mathbb Q(\sqrt{-2})$ is a fixed prime numb...

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 group of $K$ are determined by $\mathcal G^{ab}_{K}$. The converse is almost true: isomorphism type of...

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 Artin L-functions of representations associated to the common normal closure of those fields. We prov...

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 is to provide a complete description of such a list.

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 precisely, we improve the lower bounds on the maximal number
of points $N_q(g)$ for many values of the...