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Эта публикация цитируется в 40 научных статьях (всего в 40 статьях)
On exponents of homogeneous and inhomogeneous Diophantine approximation
[О показателях однородных и неоднородных диофантовых приближений]
Ya. Bugeauda, M. Laurentb
a University Louis Pasteur
b Institut de Mathématiques de Luminy
Аннотация:
В теории диофантовых приближений неоднородные задачи связаны с однородными т.н. теоремами перенесения. Мы возвращаемся к этой классической тематике, вводя новые показатели диофантова приближения. Показано, что неоднородный показатель приближения точки общего положения в $\mathbb R^n$ системой $n$ линейных форм равен обратной величине равномерного однородного показателя, связанного с системой двойственных линейных форм.
DOI:
https://doi.org/10.17323/1609-4514-2005-5-4-747-766
Полный текст:
http://www.ams.org/.../abst5-4-2005.html
 Список литературы:
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Реферативные базы данных:
  
MSC: 11J20, 11J13, 11J82
Статья поступила: 4 ноября 2004 г.
Язык публикации: английский
Образец цитирования:
Y. Bugeaud, M. Laurent, “On exponents of homogeneous and inhomogeneous Diophantine approximation”, Mosc. Math. J., 5:4 (2005), 747–766
Цитирование в формате AMSBIB
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\paper On exponents of homogeneous and inhomogeneous Diophantine approximation
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 4
\pages 747--766
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Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
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Bugeaud Ya., Laurent M., “Exponents of diophantine approximation”, Diophantine Geometry, Proceedings, CRM Series, 4, 2007, 101–121
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Bugeaud Y., “On the approximation to algebraic numbers by algebraic numbers”, Glas. Mat. Ser. III, 44:2 (2009), 323–331
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Schmidt W.M., Summerer L., “Parametric geometry of numbers and applications”, Acta Arith., 140:1 (2009), 67–91
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Bugeaud Ya., Kristensen S., “Diophantine exponents for mildly restricted approximation”, Ark. Mat., 47:2 (2009), 243–266
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Bugeaud Ya., Evertse J.-H., “Approximation of complex algebraic numbers by algebraic numbers of bounded degree”, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 8:2 (2009), 333–368
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Laurent M., “Exponents of Diophantine approximation in dimension two”, Canad. J. Math., 61:1 (2009), 165–189
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Н. Г. Мощевитин, “Сингулярные диофантовы системы А. Я. Хинчина и их применение”, УМН, 65:3(393) (2010), 43–126
 ; N. G. Moshchevitin, “Khintchine's singular Diophantine systems and their applications”, Russian Math. Surveys, 65:3 (2010), 433–511 -
Beresnevich V., Velani S., “An inhomogeneous transference principle and Diophantine approximation”, Proc. Lond. Math. Soc. (3), 101:3 (2010), 821–851
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В. В. Бересневич, С. Л. Велани, “Совместные неоднородные диофантовы приближения на многообразиях”, Фундамент. и прикл. матем., 16:5 (2010), 3–17 ; V. V. Beresnevich, S. L. Velani, “Simultaneous inhomogeneous Diophantine approximation on manifolds”, J. Math. Sci., 180:5 (2012), 531–541
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М. Лоран, “О неоднородных диофантовых приближениях и размерности Хаусдорфа”, Фундамент. и прикл. матем., 16:5 (2010), 93–101 ; M. Laurent, “On inhomogeneous Diophantine approximation and Hausdorff dimension”, J. Math. Sci., 180:5 (2012), 592–598
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Bugeaud Ya., Harrap S., Kristensen S., Velani S., “On Shrinking Targets for Z(M) Actions on Tori”, Mathematika, 56:2 (2010), 193–202
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Roy D., Zelo D., “Measures of algebraic approximation to Markoff extremal numbers”, J. London Math. Soc. (2), 83:2 (2011), 407–430
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Broderick R., Fishman L., Kleinbock D., “Schmidt's game, fractals, and orbits of toral endomorphisms”, Ergodic Theory Dynam Systems, 31:4 (2011), 1095–1107
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Laurent M., Nogueira A., “Approximation to points in the plane by SL(2,Z)-orbits”, J London Math Soc (2), 85:2 (2012), 409–429
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de Mathan B., “Linear forms at a basis of an algebraic number field”, J Number Theory, 132:1 (2012), 1–25
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Laurent M., Nogueira A., “Inhomogeneous Approximation with Coprime Integers and Lattice Orbits”, Acta Arith., 154:4 (2012), 413–427
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Schmidt W.M., Summerer L., “Diophantine Approximation and Parametric Geometry of Numbers”, Mon.heft. Math., 169:1 (2013), 51–104
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Bounemoura A., Fischler S., “A Diophantine Duality Applied to the Kam and Nekhoroshev Theorems”, Math. Z., 275:3-4 (2013), 1135–1167
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Ghosh A., Gorodnik A., Nevo A., “Diophantine Approximation and Automorphic Spectrum”, Int. Math. Res. Notices, 2013, no. 21, 5002–5058
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Shapira U., “Grids with Dense Values”, Comment. Math. Helv., 88:2 (2013), 485–506
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А. А. Илларионов, “О среднем количестве наилучших приближений линейных форм”, Изв. РАН. Сер. матем., 78:2 (2014), 61–86 ; A. A. Illarionov, “On the average number of best approximations of linear forms”, Izv. Math., 78:2 (2014), 268–292
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Fischler S., Hussain M., Kristensen S., Levesley J., “a Converse To Linear Independence Criteria, Valid Almost Everywhere”, Ramanujan J., 38:3 (2015), 513–528
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Dani S.G., Laurent M., Nogueira A., “Multi-Dimensional Metric Approximation By Primitive Points”, Math. Z., 279:3-4 (2015), 1081–1101
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Wu Y., Shamai (Shitz) Shlomo, Verdu S., “Information Dimension and the Degrees of Freedom of the Interference Channel”, IEEE Trans. Inf. Theory, 61:1 (2015), 256–279
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Ghosh A., Gorodnik A., Nevo A., “Diophantine Approximation Exponents on Homogeneous Varieties”, Recent Trends in Ergodic Theory and Dynamical Systems, Contemporary Mathematics, 631, eds. Bhattacharya S., Das T., Ghosh A., Shah R., Amer Mathematical Soc, 2015, 181–200
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Stotz D., Bolcskei H., “Degrees of Freedom in Vector Interference Channels”, IEEE Trans. Inf. Theory, 62:7 (2016), 4172–4197
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Harrap S., Moshchevitin N., “a Note on Weighted Badly Approximable Linear Forms”, Glasg. Math. J., 59:2 (2017), 349–357
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Singhal L., “Diophantine Exponents For Standard Linear Actions of Sl2 Over Discrete Rings in C”, Acta Arith., 177:1 (2017), 53–73
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Bank E., Nesharim E., Pedersen S.H., “Solution of Cassels' Problem on a Diophantine Constant Over Function Fields”, Int. Math. Res. Notices, 2017, no. 18, 5451–5474
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Bengoechea P., Moshchevitin N., “Badly Approximable Points in Twisted Diophantine Approximation and Hausdorff Dimension”, Acta Arith., 177:4 (2017), 301–314
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Ghosh A., Gorodnik A., Nevo A., “Best Possible Rates of Distribution of Dense Lattice Orbits in Homogeneous Spaces”, J. Reine Angew. Math., 745 (2018), 155–188
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Fukshansky L., Moshchevitin N., “On An Effective Variation of Kronecker'S Approximation Theorem Avoiding Algebraic Sets”, Proc. Amer. Math. Soc., 146:10 (2018), 4151–4163
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Marnat A., “About Jarnik'S-Type Relation in Higher Dimension”, Ann. Inst. Fourier, 68:1 (2018), 131–150
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Marnat A., “Note on the Spectrum of Classical and Uniform Exponents of Diophantine Approximation”, Acta Arith., 185:1 (2018), 1–8
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Johannes Schleischitz, “Diophantine approximation in prescribed degree”, Mosc. Math. J., 18:3 (2018), 491–516
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Kim D.H., Liao L., “Dirichlet Uniformly Well-Approximated Numbers”, Int. Math. Res. Notices, 2019:24 (2019), 7691–7732
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Chow S., Technau N., “Higher-Rank Bohr Sets and Multiplicative Diophantine Approximation”, Compos. Math., 155:11 (2019), 2214–2233
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Bugeaud Ya., Zhang Zh., “on Homogeneous and Inhomogeneous Diophantine Approximation Over the Fields of Formal Power Series”, Pac. J. Math., 302:2 (2019), 453–480
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Bugeaud Ya., Cheung Y., Chevallier N., “Hausdorff Dimension and Uniform Exponents in Dimension Two”, Math. Proc. Camb. Philos. Soc., 167:2 (2019), 249–284
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Ghosh A., Marnat A., “on Diophantine Transference Principles”, Math. Proc. Camb. Philos. Soc., 166:3 (2019), 415–431
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