Guillermo Mantilla-Soler

activity

20112021

most citedThe trace form over cyclic number fields

7 citations · 22 across the 16 of their papers we have counts for

collaborators

21 papers

math.NT2021

Dense generic well-rounded lattices

Camilla Hollanti, Guillermo Mantilla-Soler, Niklas Miller

It is well-known that the densest lattice sphere packings also typically have large kissing numbers. The sphere packing density maximization problem is known to have a solution amo…

math.NT2021

Density questions on arithmetic equivalence

Guillermo Mantilla-Soler

It is a classic result that two number fields have equal Dedekind zeta functions if and only if the arithmetic type of a prime $p$ is the same in both fields for almost all prime $…

math.NT2020

Bases of minimal vectors in tame lattices

Mohamed Taoufiq Damir, Guillermo Mantilla-Soler

Motivated by the behavior of the trace pairing over tame cyclic number fields, we introduce the notion of tame lattices. Given an arbitrary non-trivial lattice $L$ we con…

math.NT2019

The Shape of cyclic number fields

Wilmar Bolaños, Guillermo Mantilla-Soler

Let $m > 1$ and $d \neq = 0$ be integers such that $v_{p} (d) \neq = m$ for any prime $p$ . We construct a matrix $A (d)$ of size $(m - 1) \times (m - 1)$ depen…

math.NT2019

Theta series and number fields: theorems and experiments

Adrian Barquero-Sanchez, Guillermo Mantilla-Soler, Nathan C. Ryan

We construct certain $θ$ -series associated to number fields and prove that for number fields of degree less than equal to 4, these $θ$ -series are number field invariants. We also i…

math.NT2019

An introduction to $Γ$ -number fields

Guillermo Mantilla-Soler

It follows from generalities of quadratic forms that the spinor class of the integral trace of a number field determines the signature and the discriminant of the field. In this pa…

math.NT2019

A proof of a conjecture on trace-zero forms and shapes of number fields

Guillermo Mantilla-Soler, Carlos Rivera-Guaca

In 2012 the first named author conjectured that totally real quartic fields of fundamental discriminant are determined by the isometry class of the integral trace zero form; such c…

math.NT2019

The $(α, β) -$ ramification invariants of a number field

Guillermo Mantilla-Soler

Let $L$ be a number field. For a given prime $p$ we define integers $α_{p}^{L}$ and $β_{p}^{L}$ with some interesting arithmetic properties. For instance, $β_{p}^{L}$ is equal to $…

math.NT2019★ 7 cited

The trace form over cyclic number fields

Wilmar Bolaños, Guillermo Mantilla-Soler

In the mid 80's Conner and Perlis showed that for cyclic number fields of prime degree $p$ the isometry class of integral trace is completely determined by the discriminant. Here w…

math.NT2018

The integral trace form as a complete invariant for real $S_{n}$ number fields

Guillermo Mantilla-Soler, Carlos Rivera

In the past the first named author has studied to what extent the integral trace can characterize a number field beyond what the discriminant does. The cases of cyclic number field…

math.NT2018★ 1 cited

An $ℓ - p$ switch trick to obtain a new elementary proof of a criterion for arithmetic equivalence

Tristram Bogart, Guillermo Mantilla-Soler

Two number fields are called arithmetically equivalent if they have the same Dedekind zeta function. In the 1970's Perlis showed that this is equivalent to the condition that for a…

math.NT2018★ 6 cited

On a question of Perlis and Stuart regarding arithmetic equivalence

Guillermo Mantilla-Soler

Let $K$ be a number field. The $K$ -arithmetic type of a rational prime $ℓ$ is the tuple $A_{K} (ℓ) = (f_{1}^{K}, ..., f_{g_{ℓ}}^{K})$ of the residue degrees of $ℓ$ in $K$ , w…

math.GN2017

On a characterization of path connected topological fields

Xavier Caicedo, Guillermo Mantilla-Soler

The aim of this paper is to give a characterization of path connected topological fields, inspired by the classical Gelfand correspondence between a compact Hausdorff topological s…

math.NT2013★ 4 cited

The shape of $Z / ℓ Z$ -number fields

Guillermo Mantilla-Soler, Marina Monsurrò

Let $ℓ$ be a prime and let $L / Q$ be a Galois number field with Galois group isomorphic to $Z / ℓ Z$ . We show that the {\it shape} of $L$ is either $\f…

math.NT2013★ 1 cited

Weak arithmetic equivalence

Guillermo Mantilla-Soler

Inspired by the invariant of a number field given by its zeta function, we define the notion of {\it weak arithmetic equivalence}, and show that under certain ramification hypothes…

math.NT2013

On the Arithmetic determination of the trace

Guillermo Mantilla-Soler

Let $K$ be a number field, which is tame and non totally real. In this article we give a numerical criterion, depending only on the ramification behavior of ramified primes in $K$ ,…

math.NT2013

The spinor genus of the integral trace

Guillermo Mantilla-Soler

Let $K$ be a number field of degree at least $3$ . In this article we show that the genus of the integral trace form of $K$ contains only one spinor genus. Additionally we show that…

math.GR2011★ 2 cited

Power map permutations and symmetric differences in finite groups

Márton Hablicsek, Guillermo Mantilla-Soler

Let $G$ be a finite group. For all $a \in Z$ , such that $(a, ∣ G ∣) = 1$ , the function $ρ_{a} : G \to G$ sending $g$ to $g^{a}$ defines a permutation of the elements of $G$ . Motivated by a…

math.NT2011★ 1 cited

A space of weight one modular forms attached to totally real cubic number fields

Guillermo Mantilla-Soler

Let $d$ be a positive fundamental discriminant, and let $C_{d}$ be the set of isomorphism classes of cubic number fields of discriminant $d$ . For each $K \in \mathcal{C}_…

math.NT2011

On number fields with equivalent integral trace forms

Guillermo Mantilla-Soler

Let $K$ be a number field. The \textit{integral trace form} is the integral quadratic form given by $tr_{K / Q} (x^{2}) ∣_{O_{K}} .$ In this article we study the existence…

math.NT2011

Integral trace forms associated to cubic extensions

Guillermo Mantilla-Soler

Given a nonzero integer $d$ , we know by Hermite's Theorem that there exist only finitely many cubic number fields of discriminant $d$ . However, it can happen that two non-isomorphi…

Dense generic well-rounded lattices

Density questions on arithmetic equivalence

Bases of minimal vectors in tame lattices

The Shape of cyclic number fields

Theta series and number fields: theorems and experiments

An introduction to Γ-number fields

A proof of a conjecture on trace-zero forms and shapes of number fields

The (α,β)−ramification invariants of a number field

The trace form over cyclic number fields

The integral trace form as a complete invariant for real Sn​ number fields

An ℓ−p switch trick to obtain a new elementary proof of a criterion for arithmetic equivalence

On a question of Perlis and Stuart regarding arithmetic equivalence

On a characterization of path connected topological fields

The shape of Z/ℓZ-number fields

Weak arithmetic equivalence

On the Arithmetic determination of the trace

The spinor genus of the integral trace

Power map permutations and symmetric differences in finite groups

A space of weight one modular forms attached to totally real cubic number fields

On number fields with equivalent integral trace forms

Integral trace forms associated to cubic extensions

An introduction to $Γ$ -number fields

The $(α, β) -$ ramification invariants of a number field

The integral trace form as a complete invariant for real $S_{n}$ number fields

An $ℓ - p$ switch trick to obtain a new elementary proof of a criterion for arithmetic equivalence

The shape of $Z / ℓ Z$ -number fields