Zobrazeno 1 - 10
of 139
pro vyhledávání: '"Kala, Vítězslav"'
Given a totally real number field $F$, we show that there are only finitely many totally real extensions of $K$ of a fixed degree that admit a universal quadratic form defined over $F$. We further obtain several explicit classification results in the
Externí odkaz:
http://arxiv.org/abs/2407.20781
Autor:
Kala, Vitezslav, Prakash, Om
We study the universality of forms of degree greater than 2 over rings of integers of totally real number fields. We show that such universal forms always exist, but cannot be characterized by any variant of the 290-Theorem of Bhargava-Hanke.
Co
Co
Externí odkaz:
http://arxiv.org/abs/2405.10660
We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this ph
Externí odkaz:
http://arxiv.org/abs/2404.12844
Autor:
Kala, Vítězslav, Man, Siu Hang
We establish a new connection between sails, a key notion in the geometric theory of generalised continued fractions, and arithmetic of totally real number fields, specifically, universal quadratic forms and additively indecomposable integers. Our ma
Externí odkaz:
http://arxiv.org/abs/2403.18390
Autor:
Kala, Vítězslav, Yatsyna, Pavlo
We classify all totally real number fields of degree at most 5 that admit a universal quadratic form with rational integer coefficients; in fact, there are none over the previously unsolved cases of quartic and quintic fields. This fully settles the
Externí odkaz:
http://arxiv.org/abs/2402.03850
Autor:
Kala, Vítězslav, Melistas, Mentzelos
We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption that the c
Externí odkaz:
http://arxiv.org/abs/2311.12911
We show that if a universal quadratic form exists over an infinite degree, totally real extension of the field of rationals $\mathbb{Q}$, then the set of totally positive integers in the extension does not have the Northcott property. In particular,
Externí odkaz:
http://arxiv.org/abs/2308.16721
Autor:
Kala, Vítězslav, Šíma, Lucien
Publikováno v:
Algebra Universalis 85 (2024), article 24, 19 pp
We study ideal-simple commutative semirings and summarize the results giving their classification, in particular when they are finitely generated. In the principal case of (para)semifields, we then consider their minimal number of generators and show
Externí odkaz:
http://arxiv.org/abs/2307.07287
Publikováno v:
Expo. Math. 42 (2024), article 125571, 36 pp
We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it to prove th
Externí odkaz:
http://arxiv.org/abs/2307.00898
Autor:
Kala, Vítězslav, Zindulka, Mikuláš
Publikováno v:
Ramanujan J. 64 (2024), 537-551
We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $\beta$. We prove that if $\beta$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $\beta$ is larger t
Externí odkaz:
http://arxiv.org/abs/2305.16688