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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">vestifm</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Национальной академии наук Беларуси. Серия физико-математических наук</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1561-2430</issn><issn pub-type="epub">2524-2415</issn><publisher><publisher-name>The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.29235/1561-2430-2018-54-1-24-29</article-id><article-id custom-type="elpub" pub-id-type="custom">vestifm-294</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МАТЕМАТИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICS</subject></subj-group></article-categories><title-group><article-title>ОБОБЩЕНИЕ ЛЕММЫ ГЕЛЬФОНДА НА ЦИЛИНДРЫ В ПОЛЕ р-АДИЧЕСКИХ ЧИСЕЛ</article-title><trans-title-group xml:lang="en"><trans-title>GENERALIZATION OF GELFOND’S LEMMA TO p-ADIC CYLINDERS</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кемеш</surname><given-names>О. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Kemesh</surname><given-names>O. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p> старший преподаватель кафедры высшей математики факультета предпринимательства и управления</p></bio><email xlink:type="simple">oksana.kemesh@tut.by</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Белорусский государственный аграрный технический университет, Минск</institution></aff><aff xml:lang="en"><institution>Belarusian State Agrarian Technical University, Minsk</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2018</year></pub-date><pub-date pub-type="epub"><day>05</day><month>04</month><year>2018</year></pub-date><volume>54</volume><issue>1</issue><fpage>24</fpage><lpage>29</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Кемеш О.Н., 2018</copyright-statement><copyright-year>2018</copyright-year><copyright-holder xml:lang="ru">Кемеш О.Н.</copyright-holder><copyright-holder xml:lang="en">Kemesh O.N.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://vestifm.belnauka.by/jour/article/view/294">https://vestifm.belnauka.by/jour/article/view/294</self-uri><abstract><p>.</p></abstract><kwd-group xml:lang="ru"><kwd>мера Хаара</kwd><kwd>лемма Гельфонда</kwd><kwd>размерность Хаусдорфа</kwd><kwd>поле p-адических чисел</kwd><kwd>p-адический цилиндр</kwd><kwd>диофантовы приближения</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Haar’s measure</kwd><kwd>Gelfond’s lemma</kwd><kwd>Hausdorff’s dimension</kwd><kwd>p-adic numbers</kwd><kwd>p-adic cylinder</kwd><kwd>Diophantine approximation</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Гельфонд, А. О. Трансцендентные и алгебраические числа / А. О. Гельфонд. – 2-е изд. – М.: URSS, 2006. – 224 с.</mixed-citation><mixed-citation xml:lang="en">Gelfond А. О. Transcendental and algebraic numbers. 2nd ed. Moscow, URSS, 2006. 224 p. (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Bernik, V. Application of the Hausdorff dimension in the theory of Diophantine approximations / V. Bernik // Acta Arithmetica. – 1983. – Vol. 42, № 3. – P. 219–253.</mixed-citation><mixed-citation xml:lang="en">Bernik V. Application of the Hausdorff dimension in the theory of Diophantine approximations. Acta Arithmetica, 1983, vol. 42, no. 3, pp. 219–253.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Baker, A. Diophantine approximation and Hausdorff dimension / A. Baker, W. M. Schmidt // Proc. London Math. Soc. – 1970 – Vol. s3-21, № 1. – P. 1–11.</mixed-citation><mixed-citation xml:lang="en">Baker A., Schmidt W. M. Diophantine approximation and Hausdorff dimension. Proceedings of the London Mathematical Society, 1970, vol. s3-21, no. 1, pp. 1–11. Doi: 10.1112/plms/s3-21.1.1</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Bernik, V. A new connection between metnic theory of Diophantine approximations and distribution of algebraic numbers / V. Bernik, F. Götze // Contemp. Math. – 2015. – P. 33–45.</mixed-citation><mixed-citation xml:lang="en">Bernik V., Götze F. A new connection between metnic theory of Diophantine approximations and distribution of algebraic numbers. Contemporary Mathematics, 2015, pp. 33–45. Doi: 10.1090/conm/631/12594</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Bernik, V. On the divisibility of the discriminant of an integral polynomia by prime powers/ V. Bernik, F. Götze, O. Kukso // Lith. Math. J. – 2008. – Vol. 48, № 4. – P. 380–396.</mixed-citation><mixed-citation xml:lang="en">Bernik V., Götze F., Kukso O. On the divisibility of the discriminant of an integral polynomia by prime powers. Lithuanian Mathematical Journal, 2008, vol. 48, no. 4, pp. 380–396. Doi: 10.1007/s10986-008-9025-5</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Берник, В. И. Приближение нуля целочисленными полиномами в пространстве ××p / В. И. Берник, Н. Калоша // Вес. Нац. акад. навук Беларусi. Сер. фiз.-мат. навук. – 2004. – № 1. – P. 121–123.</mixed-citation><mixed-citation xml:lang="en">Bernik, V. I., Kalosha N. Zero approximation by integer polynomials in the space ××p Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2004, no. 1, pp. 121–123 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Bernik, V. Simultaneous Diophantine approximation in the real, complex and p-adic fields / V. Bernik, N. Budarina, H. Dickinson // Math. Proc. Cambridge Philos. Soc. – 2010. – Vol. 149, № 2. – P. 193–216.</mixed-citation><mixed-citation xml:lang="en">Bernik V., Budarina N., Dickinson H. Simultaneous Diophantine approximation in the real, complex and p-adic fields. Mathematical Proceedings of the Cambridge Philosophical Society, 2010, vol. 149, no. 2, pp. 193–216. Doi: 10.1017/s0305004110000162</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Спринджук, В. Г. Проблема Малера в метрической теории чисел / В. Г. Спринджук. – М.: Наука и техника, 1967. – 184 с.</mixed-citation><mixed-citation xml:lang="en">Sprindzhuk V. G. Mahler‘s problem in metric number theory. Moscow, Nauka i tekhnika Publ., 1967. 184 p. (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Берник, В. И. О точном порядке приближения нуля значениями целочисленных многочленов / В. И. Берник // Acta Arithmetica. – 1989. – Vol. 53, № 1. – P. 17–28.</mixed-citation><mixed-citation xml:lang="en">Bernik V. I. About the exact order of approximation of zero by values of integral polynomials. Acta Arithmetica, 1989, vol. 53 no. 1, pp. 17–28 (in Russian). Doi: 10.4064/aa-53-1-17-28</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Bernik, V. Metric Diophantine Approximation on Manifolds / V. Bernik, M. Dodson. – Cambridge University Press, 1999. – 172 p.</mixed-citation><mixed-citation xml:lang="en">Bernik V., Dodson M. Metric Diophantine approximation on manifolds. Cambridge University Press, 1999. 172 p. Doi: 0.1017/cbo9780511565991</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
