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Tr. Mat. Inst. Steklova, 2011, Volume 275, Pages 227–239 (Mi tm3340)  

This article is cited in 7 scientific papers (total in 7 papers)

Transference inequalities for multiplicative Diophantine exponents

Oleg N. German

Moscow State University, Moscow, Russia

Abstract: We prove inequalities for multiplicative analogues of Diophantine exponents; these inequalities are similar to the ones known in the classical case. Particularly, we show that a matrix is badly approximable if and only if its transpose is badly approximable and establish some inequalities connecting multiplicative exponents with ordinary ones.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2011, 275, 216–228

Bibliographic databases:

UDC: 511.4
Received in December 2010
Language:

Citation: Oleg N. German, “Transference inequalities for multiplicative Diophantine exponents”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Tr. Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 227–239; Proc. Steklov Inst. Math., 275 (2011), 216–228

Citation in format AMSBIB
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\by Oleg~N.~German
\paper Transference inequalities for multiplicative Diophantine exponents
\inbook Classical and modern mathematics in the wake of Boris Nikolaevich Delone
\bookinfo Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth
\serial Tr. Mat. Inst. Steklova
\yr 2011
\vol 275
\pages 227--239
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. N. German, “Plokho priblizhaemye matritsy i diofantovy eksponenty”, Chebyshevskii sb., 14:4 (2013), 38–79  mathnet
    2. O. N. German, K. G. Evdokimov, “A strengthening of Mahler's transference theorem”, Izv. Math., 79:1 (2015), 60–73  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Thai Hoang Le, Vaaler J.D., “Sums of Products of Fractional Parts”, Proc. London Math. Soc., 111:3 (2015), 561–590  crossref  mathscinet  zmath  isi
    4. Le T.H., Vaaler J.D., “Multiplicatively Badly Approximable Matrices in Fields of Power Series”, Proc. Amer. Math. Soc., 143:9 (2015), PII S0002-9939(2015)12570-1, 3791–3800  crossref  mathscinet  zmath  isi  elib
    5. Marnat A., “There is no analogue to Jarník's relation for twisted Diophantine approximation”, Mon.heft. Math., 181:3 (2016), 675–688  crossref  mathscinet  zmath  isi  scopus
    6. Ghosh A., Marnat A., “On Diophantine Transference Principles”, Math. Proc. Camb. Philos. Soc., 166:3 (2019), 415–431  crossref  mathscinet  zmath  isi  scopus
    7. Fregoli R., “Sums of Reciprocals of Fractional Parts”, Int. J. Number Theory, 15:4 (2019), 789–797  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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