Algebraic Number Theory and Diophantine Analysis
DOI: 10.1515/9783110801958.311
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Distribution of Kronecker sequences

Abstract: This short and simple communication is motivated by recent papers [1,5,15] as well as by the discussion on Poincaré's and Bohl's results in [35], Chapter 8. We give a brief analysis of an example constructed by Poincaré and its recent generalisations. Most of the constructions under consideration are well-known. In this note, we just wanted to bring all the results together and give a general and improved multi-dimensional formulation of a recent result by A. Kochergin [15], prove non-existence of a universal … Show more

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Cited by 3 publications
(13 citation statements)
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“…In particular, this shows that there are singular matrices A with λ(Bad A ) = 0. The definition of the Diophantine class of matrices is stated in terms of the sequence of best approximations and is tightly related and motivated by the discussions in the papers [Mos23] and [Kim23]. We note that in [Kim23], another complementary Diophantine class is defined, which is a subclass of the singular matrices, and it is proved there that for such matrices A one has λ(Bad A ) = 1.…”
Section: If One Defines a Variant Bad +mentioning
confidence: 99%
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“…In particular, this shows that there are singular matrices A with λ(Bad A ) = 0. The definition of the Diophantine class of matrices is stated in terms of the sequence of best approximations and is tightly related and motivated by the discussions in the papers [Mos23] and [Kim23]. We note that in [Kim23], another complementary Diophantine class is defined, which is a subclass of the singular matrices, and it is proved there that for such matrices A one has λ(Bad A ) = 1.…”
Section: If One Defines a Variant Bad +mentioning
confidence: 99%
“…The proof of the following result is motivated by [Kim23, Theorem 1.7] and is based on an application of Minkowski successive minima theory and modifies the proof from [Mos23].…”
Section: Recall That In Our Notationmentioning
confidence: 99%
“…[101]) и Н. Г. Мощевити-ным в общем случае (см. [102], [103]). Ниже мы приведем формулировки этих результатов и дадим некоторые комментарии.…”
Section: задача в в козловаunclassified
“…Доказательства теоремы 60 можно найти в работах автора [102] и [103]. Од-нако там она сформулирована с худшим значением показателя гладкости w(m).…”
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