Results 41 to 50 of about 157,707 (146)

Approximation of number π by algebraic numbers from special fields

Journal of Number Theory, 1977
Abstract The estimate from below of the modulus of the difference between π and algebraic numbers from the fields generated by the roots of unity is made.
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Simultaneous approximation to algebraic numbers by rationals

Acta Mathematica, 1970
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Description of the related and resonant states of the nuclei (_3^6)Li of the lie in the method of resonant groups

Physical Sciences and Technology, 2018
To consider the interactions between light nuclei, as well as the nature of the nuclear forces between them, and the test was made of the coupled and resonant positions of the nucleus (_3^6)Li using the technique of the "Algebraic version of the ...
N.K. Kalzhigitov, K. Kato, V.S. Vasilevsky, V.O. Kurmangaliyeva, N. Zh. Takibayev   +4 more
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On approximations of solutions of the equation P(z,lnz) = 0 by algebraic numbers

Moscow Journal of Combinatorics and Number Theory, 2020
Let \(d_1\) and \(d_2\) be positive integers. Let \(P(x,y)\in\mathbb Z[x,y]\) such that \(\deg_x =d_1\) and \(\deg_y =d_2\). Then, the authors prove that for every \(\varepsilon >0\) and \(r>0\), the inequality \[|P(\theta,\log\theta)|
Galochkin, Alexander, Godunova, Anastasia   +1 more
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Effective approximation to complex algebraic numbers by quadratic numbers

Canadian Mathematical Bulletin
AbstractWe establish an effective improvement on the Liouville inequality for approximation to complex nonreal algebraic numbers by quadratic complex algebraic numbers.
Prajeet Bajpai, Yann Bugeaud
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Effective simultaneous approximation of complex numbers by conjugate algebraic integers [PDF]

Acta Arithmetica, 1993
Soient \(\varepsilon>0\) et \(z_ 1,\dots,z_ n\in\mathbb{C}\), \(n\) (\(\geq 1\)) nombres complexes distincts. Alors il existe un polynôme unitaire (monic) irréductible de degré \(n+1\) à coefficients dans \(\mathbb{Z}[i]\) dont les racines \(\zeta_ 1,\dots,\zeta_{n+1}\) vérifient \(| z_ j- \zeta_ j|
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SIMULTANEOUS APPROXIMATION BY CONJUGATE ALGEBRAIC NUMBERS IN FIELDS OF TRANSCENDENCE DEGREE ONE [PDF]

International Journal of Number Theory, 2005
We present a general result of simultaneous approximation to several transcendental real, complex or p-adic numbers ξ1, …, ξt by conjugate algebraic numbers of bounded degree over ℚ, provided that the given transcendental numbers ξ1, …, ξt generate over ℚ a field of transcendence degree one. We provide sharper estimates for example when ξ1, …, ξt form
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On simultaneous approximations of two algebraic numbers by rationals

Acta Mathematica, 1967
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A note on elliptic functions and approximation by algebraic numbers of bounded degree [PDF]

Annales de la Faculté des sciences de Toulouse : Mathématiques, 1983
Let p be a Weierstrass elliptic function with algebraic invariants g2 and g3. By a counterexample it is shown that lower bounds for the simultaneous approximation of p(a), b and p(ab) by algebraic numbers of bounded degree cannot be given without and added hypothesis on the numbers beta approximating b.
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Approximation to certain transcendental decimal fractions by algebraic numbers

Journal of Number Theory, 1991
For a positive integer \(g\geq 2\) consider the number \(M(g)=0.(1)_ g(2)_ g...(n)_ g...\) where for \(n\in {\mathbb{N}}\) \((n)_ g\) means digit representation of n to base g and \(0.(1)_ g(2)_ g...\) means digit representation of the real M(g) to base g. It is known that M(g) is transcendental. The author gives estimates for Mahler's function \(w_ d\)
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