### Recent Submissions

• #### Hopf-Galois module structure of quartic Galois extensions of Q ﻿

(2022-09)
Article
Open Access
Given a quartic Galois extension L/Q of number fields and a Hopf-Galois structure H on L/Q, we study the freeness of the ring of integers OL as module over the associated order AH in H. For the classical Galois structure ...
• #### Induced Hopf Galois structures and their local Hopf Galois modules ﻿

(2020-09)
Article
Open Access
The regular subgroup determining an induced Hopf Galois structure for a Galois extension L/K is obtained as direct product of the corresponding regular groups of the inducing subextensions. We describe here the attached ...
• #### An inverse Jacobian algorithm for Picard curves ﻿

(Springer, 2021-06-01)
Article
Open Access
We study the inverse Jacobian problem for the case of Picard curves over C. More precisely, we elaborate on an algorithm that, given a small period matrix O¿C3×3 corresponding to a principally polarized abelian threefold ...
• #### Satins, lattices, and extended Euclid's algorithm ﻿

(2021-01-01)
Article
Open Access
Motivated by the design of satins with draft of period m and step a, we draw our attention to the lattices L(m,a)=¿(1,a),(0,m)¿ where 1=a<m are integers with gcd(m,a)=1. We show that the extended Euclid's algorithm applied ...
• #### Every integer can be written as a square plus a squarefree ﻿

(2021-12-30)
Article
Restricted access - publisher's policy
In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asymptotic formula for the number of representations of an integer in ...
• #### A study of the separating property in Reed-Solomon codes by bounding the minimum distance ﻿

(2022-02)
Article
Open Access
According to their strength, the tracing properties of a code can be categorized as frameproof, separating, IPP and TA. It is known that, if the minimum distance of the code is larger than a certain threshold then the TA ...
• #### Derived Beilinson-Flach elements and the arithmetic of the adjoint of a modular form ﻿

(2021-03-15)
Article
Open Access
Kings, Lei, Loeffler and Zerbes constructed in [LLZ], [KLZ1] a three-variable Euler system ¿(g,h) of Beilinson–Flach elements associated to a pair of Hida families (g,h) and exploited it to obtain applications to the ...
• #### On the L-invariant of the adjoint of a weight one modular form ﻿

(2021-01-01)
Article
Open Access
The purpose of this article is proving the equality of two natural L -invariants attached to the adjoint representation of a weight one cusp form, each defined by purely analytic, respectively, algebraic means. The proof ...
• #### Primes represented by quadratic polynomials via exceptional characters ﻿

(Springer Nature, 2021-08-01)
Article
Open Access
We estimate the number of primes represented by a general quadratic polynomial with discriminant ¿, assuming that the corresponding real character is exceptional.
• #### Lazlo Lovász i Avi Widergson: premis Abel 2021 ﻿

(Societat Catalana de Matemàtiques (SCM), 2021-12-14)
Article
Open Access
El dia 17 de març l’Acadèmia de Ciències Noruega va anunciar que el Premi Abel 2021 s’atorgava a Laszló Lovász i Avi Widgerson per, segons es llegeix de la laudatio del premi, “. . . les seves contribucions fonamentals a ...
• #### Of limit key polynomials ﻿

(2021-04-01)
Article
Open Access
Let ν be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in a field K. We prove comparison theorems between MacLane-Vaquié key polynomials for valuations μ ≤ν and abstract key polynomials for ...
• #### L'aprenentatge automàtic (machine learning): una projecció de les matemàtiques en el món industrial i empresarial ﻿

(Societat Catalana de Matemàtiques (SCM), 2020-02)
Article
Open Access