On the approximation of numbers connected with $\operatorname{cn} z$ (in Ukrainian) |
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| Author |
Department of Mechanics and Mathematics, Lviv University,
Universytetska
1, Lviv, 290602, Ukraine
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| Abstract |
Let $\operatorname{cn} z$, $\omega$, $\omega'$ and $\varkappa$ be the notations of the Jacobi elliptic function theory;
let $\beta$ be any complex number different from the poles of $\operatorname{cn} z$. We estimate
from below the simultaneous approximation of $\varkappa$, $\omega$,
$\omega'$, $\beta$ and $\operatorname{cn} \beta$.
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| Keywords |
Jacobi elliptic functions, simultaneous approximation, lower estimate
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| DOI |
doi:10.30970/ms.6.1.17-22
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Reference |
1. Гурвиц А., Курант Р. Теория функций. – М.: Наука, 1968. 648с.
2. Холявка Я.М. Деякi властивостi елiптичних функцiй Якобi, (II) // Деп. в ДНТБ України 28.10.1993, №2144–УК93, 10с. 3. Холявка Я.М. О совместных приближениях инвариантов эллиптической функции алгебраическими числами // Диофантовы приближения, ч.2, Изд. МГУ, 1986, С.114–121. 4. Reyssat E. Approximation algebrique de nombres lies aux fonctions elliptique et exponentielle // Bull. Soc. Math. France. 1980. №1. P.47–79. 5. Фельдман Н.И. Седьмая проблема Гильберта. – М.: Изд-во МГУ, 1982. 311с. 6. Masser D. Elliptic functions and transcendence // Lect. Notes Math. 1975. V.437. P.1–143. 7. Brownawell W.D., Masser D.W. Multiplicity estimates for analitic functions, (I) // J. Reine Angew. Math. 1980. V.314. P.200–216. Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine |
| Pages |
17-22
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| Volume |
6
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| Issue |
1
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| Year |
1996
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |