Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Vladimir Petrovich Platonov"'
Publikováno v:
Trudy Matematicheskogo Instituta imeni V.A. Steklova. 320:278-286
Исследуется проблема описания свободных от квадратов многочленов $f(x)$ нечетной степени с периодическим разложением $\sqrt {f(x)}$ в функцион
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::04e3732bff81cfc65e260e70b6fe5a0a
https://doi.org/10.4213/tm4283
https://doi.org/10.4213/tm4283
Autor:
Fedor Alekseevich Bogomolov, Фeдор Алексеевич Богомолов, Anatolii Moiseevich Vershik, Sergei Vladimirovich Vostokov, Sergey Olegovich Gorchinskiy, Alexander Borisovich Zheglov, Yuri Gennad'evich Zarhin, Sergei Vladimirovich Konyagin, Victor Stepanovich Kulikov, Yuri Valentinovich Nesterenko, Dmitri Olegovich Orlov, Denis Vasilievich Osipov, Ivan Alexandrovich Panin, Vladimir Petrovich Platonov, Vladimir Leonidovich Popov, Yuri Gennadievich Prokhorov, Aleksandr Leonidovich Smirnov
Publikováno v:
Uspekhi Matematicheskikh Nauk. 78:165-169
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dc7b9e8afbbd775b10f0bc39b28a8689
https://doi.org/10.4213/rm10109
https://doi.org/10.4213/rm10109
Publikováno v:
Математический сборник. 213:139-170
Получено полное описание полей $\mathbb K$, являющихся расширениями $\mathbb Q$ степени не более $3$, и кубических многочленов $f \in\mathbb K[x]$, для котор
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a5e0820b56fb42e217be9b116bd77974
https://doi.org/10.4213/sm9578
https://doi.org/10.4213/sm9578
Publikováno v:
Doklady Mathematics. 102:487-492
We obtain a complete description of cubic polynomials f over algebraic number fields $$\mathbb{K}$$ of degree $$3$$ over $$\mathbb{Q}$$ for which the continued fraction expansion of $$\sqrt f $$ in the field of formal power series $$\mathbb{K}((x))$$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ccf867f67e03e9ba49f6b6d4115ed3c0
https://doi.org/10.1134/s1064562420060137
https://doi.org/10.1134/s1064562420060137
Publikováno v:
Doklady Mathematics. 102:288-292
We obtain a complete description of fields $$\mathbb{K}$$ that are quadratic extensions of $$\mathbb{Q}$$ and of cubic polynomials $$f \in \mathbb{K}[x]$$ for which a continued fraction expansion of $$\sqrt f $$ in the field of formal power series $$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::df447e01f3e1e5a9b2159827e1f28d96
https://doi.org/10.1134/s1064562420040249
https://doi.org/10.1134/s1064562420040249
Publikováno v:
Doklady Mathematics. 100:440-444
For a field k of characteristic 0, up to a natural equivalence relation, it is proved that the number of nontrivial elliptic fields $$k(x)(\sqrt f )$$ with a periodic continued fraction expansion of $$\sqrt f \in k((x))$$ for which the corresponding
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::60e56229bbd65889a2c050110b991818
https://doi.org/10.1134/s1064562419050119
https://doi.org/10.1134/s1064562419050119
Publikováno v:
Доклады Академии наук. 486:280-286
This article proves the equivalence theorem for the following conditions: the periodicity of continued fractions of a generalized type for key elements hyperelliptic field L, the existence in the hyperelliptic field L of nontrivial S-units for sets S
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::23d28c2ffc25738ab1040f17359aad7b
https://doi.org/10.31857/s0869-56524863280-286
https://doi.org/10.31857/s0869-56524863280-286
Publikováno v:
Chebyshevskii sbornik. 20:246-258
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1d0352a543586cb678b3940ff84e9564
https://doi.org/10.22405/2226-8383-2018-20-1-246-258
https://doi.org/10.22405/2226-8383-2018-20-1-246-258
Publikováno v:
Doklady Mathematics. 98:641-645
We prove the finiteness of the set of square-free polynomials f ∈ k[x] of odd degree distinct from 11 considered up to a natural equivalence relation for which the continued fraction expansion of the irrationality $$\sqrt {f\left( x \right)} $$ in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f78bd36a1aacae02066b7a6b8de49135
https://doi.org/10.1134/s1064562418070281
https://doi.org/10.1134/s1064562418070281
Publikováno v:
Doklady Mathematics. 98:430-434
We give a description of the cubic polynomials f(x) with coefficients in the quadratic number fields $$\mathbb{Q}(\sqrt{5})$$ and $$\mathbb{Q}(\sqrt{-15})$$ for which the continued fraction expansion of the irrationality $$\sqrt {f\left( x \right)} $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::81fd4e10e95ff1cd88366e22fbd7f5d6
https://doi.org/10.1134/s1064562418060091
https://doi.org/10.1134/s1064562418060091