Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Vítězslav Kala"'
Autor:
Vítězslav Kala, Tomáš Hejda
Publikováno v:
Journal of Number Theory. 234:140-152
A positive quadratic form is $(k,\ell)$-universal if it represents all the numbers $kx+\ell$ where $x$ is a non-negative integer, and almost $(k,\ell)$-universal if it represents all but finitely many of them. We prove that for any $k,\ell$ such that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::953a324647ac15763c28fcd3fd5ee13a
https://doi.org/10.1016/j.jnt.2021.09.017
https://doi.org/10.1016/j.jnt.2021.09.017
For a given positive integer $k$, we prove that there are at least $x^{1/2-o(1)}$ integers $d\leq x$ such that the real quadratic fields $\mathbb Q(\sqrt{d+1}),\dots,\mathbb Q(\sqrt{d+k})$ have class numbers essentially as large as possible.
7 p
7 p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::078f01b551490eebf582e414724f5be2
http://arxiv.org/abs/2111.11549
http://arxiv.org/abs/2111.11549
Autor:
Vítězslav Kala, Tomáš Hejda
Publikováno v:
manuscripta mathematica. 163:263-278
Let $K=\mathbb Q(\sqrt D)$ be a real quadratic field. We consider the additive semigroup $\mathcal O_K^+(+)$ of totally positive integers in $K$ and determine its generators (indecomposable integers) and relations; they can be nicely described in ter
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::68b993d650eb0e2607d5df4a3f17d6f8
https://doi.org/10.1007/s00229-019-01143-8
https://doi.org/10.1007/s00229-019-01143-8
Autor:
Tomáš Vávra, Vítězslav Kala
Publikováno v:
Monatshefte für Mathematik. 188:109-119
We study periodic representations in number systems with an algebraic base $$\beta $$ (not a rational integer). We show that if $$\beta $$ has no Galois conjugate on the unit circle, then there exists a finite integer alphabet $$\mathcal A$$ such tha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::84a26071c1e6a8cab9734630f85efe5d
https://doi.org/10.1007/s00605-017-1151-x
https://doi.org/10.1007/s00605-017-1151-x
Autor:
Vítězslav Kala, Petr Glivický
Publikováno v:
Mathematical Logic Quarterly
We study Fermat's Last Theorem and Catalan's conjecture in the context of weak arithmetics with exponentiation. We deal with expansions (B,e) of models of arithmetical theories (in the language L=(0,1,+,x
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5a9f25aba4c8ee9351ee7628d86d7a75
https://doi.org/10.1002/malq.201500069
https://doi.org/10.1002/malq.201500069
Autor:
Miroslav Korbelář, Vítězslav Kala
We prove that a commutative parasemifield S is additively idempotent provided that it is finitely generated as a semiring. Consequently, every proper commutative semifield T that is finitely generated as a semiring is either additively constant or ad
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::99cd396eb1286cee1fb2a4e9cca047d6
http://arxiv.org/abs/1910.02457
http://arxiv.org/abs/1910.02457
Autor:
Pavlo Yatsyna, Vítězslav Kala
We study totally real number fields that admit a universal quadratic form whose coefficients are rational integers. We show that $\mathbb Q(\sqrt 5)$ is the only such real quadratic field, and that among fields of degrees 3, 4, 5, and 7 which have pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ad9f2f2ba0df6951c22d208a5bd7536
http://arxiv.org/abs/1808.02262
http://arxiv.org/abs/1808.02262
Autor:
Valentin Blomer, Vítězslav Kala
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 159:239-252
Given any positive integer M, we show that there are infinitely many real quadratic fields that do not admit universal quadratic forms in M variables.
Comment: Some arguments simplified and more streamlined relative to the first version
Comment: Some arguments simplified and more streamlined relative to the first version
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::50734f925061086e42576e59c5371c9e
https://doi.org/10.1017/s030500411500033x
https://doi.org/10.1017/s030500411500033x
Autor:
Vítězslav Kala
Publikováno v:
J. Commut. Algebra 9, no. 3 (2017), 387-412
A lattice-ordered group (an $\ell$-group) $G(\oplus, \vee, \wedge)$ can be naturally viewed as a semiring $G(\vee,\oplus)$. We give a full classification of (abelian) $\ell$-groups which are finitely generated as semirings, by first showing that each
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11bd5adf2324a54de72862135712b3e4
https://doi.org/10.1216/jca-2017-9-3-387
https://doi.org/10.1216/jca-2017-9-3-387
Autor:
Valentin Blomer, Vítězslav Kala
We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field $\mathbb Q(\sqrt D)$ and obtain lower and upper bounds for it in terms of certain sums of coefficients of t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c0a403eb07986658722afc4f5f27be8f
http://arxiv.org/abs/1705.03671
http://arxiv.org/abs/1705.03671