Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Carlo Pagano"'
Publikováno v:
Journal of the Institute of Mathematics of Jussieu. 21:1543-1570
We show that for $100\%$ of the odd, square free integers $n> 0$ , the $4$ -rank of $\text {Cl}(\mathbb{Q} (i, \sqrt {n}))$ is equal to $\omega _3(n) - 1$ , where $\omega _3$ is the number of prime divisors of n that are $3$ modulo $4$ .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a80e9726d0121477921619ba1c97ce0f
https://doi.org/10.1017/s1474748020000651
https://doi.org/10.1017/s1474748020000651
Autor:
Daniel El-Baz, Carlo Pagano
Publikováno v:
Journal of Group Theory
We prove the existence of a limiting distribution for the appropriately rescaled diameters of random undirected Cayley graphs of finite nilpotent groups of bounded rank and nilpotency class, thus extending a result of Shapira and Zuck which dealt wit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da6c8be881603140ab04abaac3ff2d62
https://hdl.handle.net/21.11116/0000-000B-1D99-921.11116/0000-0009-520C-E
https://hdl.handle.net/21.11116/0000-000B-1D99-921.11116/0000-0009-520C-E
Autor:
Andrea Ferraguti, Carlo Pagano
Publikováno v:
International Mathematics Research Notices
In this paper, we prove several results on finitely generated dynamical Galois groups attached to quadratic polynomials. First we show that, over global fields, quadratic post-critically finite polynomials are precisely those having an arboreal repre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a47d91e7439c869346b885c7522af168
http://arxiv.org/abs/2004.02847
http://arxiv.org/abs/2004.02847
Autor:
Peter Koymans, Carlo Pagano
Publikováno v:
Mathematika
Let $K$ be a multiquadratic extension of $\mathbb{Q}$ and let $\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors \cite{KP} gave a bound for $|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of $K$ and the number of ramifying primes
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a18b10c4f6c7a21345ba50d01056932
Autor:
Peter Koymans, Carlo Pagano
Publikováno v:
The Quarterly Journal of Mathematics. 68:923-934
Let $K$ be a field of characteristic $p > 0$ and let $G$ be a subgroup of $K^\ast \times K^\ast$ with $\text{dim}_\mathbb{Q}(G \otimes_\mathbb{Z} \mathbb{Q}) = r$ finite. Then Voloch proved that the equation $ax + by = 1 \text{ in } (x, y) \in G$ for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f68f22c4e4b47f9532dbf6589eed0969
https://doi.org/10.1093/qmath/hax007
https://doi.org/10.1093/qmath/hax007
Autor:
Peter Koymans, Carlo Pagano
Publikováno v:
International Mathematics Research Notices
In $1801$, Gauss found an explicit description, in the language of binary quadratic forms, for the $2$-torsion of the narrow class group and dual narrow class group of a quadratic number field. This is now known as Gauss's genus theory. In this paper
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2cfd428ffaea3d540b2feb498797717f
Autor:
Peter Koymans, Carlo Pagano
Publikováno v:
Acta Arithmetica
In this article we study the three-variable unit equation $x + y + z = 1$ to be solved in $x, y, z \in \mathcal{O}_S^\ast$, where $\mathcal{O}_S^\ast$ is the $S$-unit group of some global function field. We give upper bounds for the height of solutio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::712bd12dcb44384c606fe34a0dbba27d
http://arxiv.org/abs/1806.01614
http://arxiv.org/abs/1806.01614
Autor:
Carlo Pagano, Peter Koymans
Publikováno v:
Journal of the European Mathematical Society
Using a recent breakthrough of Alexander Smith, we prove that $l^\infty$-class groups of cyclic degree $l$ fields have the distribution conjectured by Gerth under GRH.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::97af593a433250d782a0d68e5850c9e9
Autor:
Carlo Pagano
Publikováno v:
Journal of Algebra
We show how to use the combinatorial notion of jump sets to parametrize the possible structures of the group of principal units of local fields, viewed as filtered modules. We establish a natural bijection between the set of jump sets and the orbit s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::917d991034036ce9db7526fee9ead3be
Autor:
Koen de Boer, Carlo Pagano
Publikováno v:
ISSAC
In the recent PhD thesis of Bouw, an algorithm is examined that computes the group structure of the principal units of a p-adic number field completion. In the same thesis, this algorithm is used to compute Hilbert norm residue symbols. In the presen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a875749715ad628eb969309a3007354a
https://doi.org/10.1145/3087604.3087637
https://doi.org/10.1145/3087604.3087637