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On the estimates of the algebraic independence measures of the values of E-functions

Published online by Cambridge University Press:  09 April 2009

A. B. Shidlovskii
Affiliation:
Department of MathematicsMoscovskii UniversityMehmat, Moscow, 117234 USSR
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Abstract

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The work establishes the estimates of linear independence, transcendence, and algebraic independence measures of the values at algebraic points of a set of E-functions, satisfying linear differential equations with coefficients from C(z), rather close to their natural bounds.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Φеeлbдmah, H.и., Шobck, A. Б. (1967), ‘Paзиtиe и cobpemehhoe coctЯhииe Teopи Tpahcцehдehthbixehthbix чиceл’, Ycnexu mamem. Hayk 22 (3), 381.Google Scholar
[2]ШидЛobckmЙ, A. Б. 1973, ‘б apиφmetиЧeckиx cbийctbax Чehй ahaлaиx Φyhkци’, Tpy∂bl MиAH CCCP um. B. A. Cmekλßa 132, 169202Google Scholar
[3]Шидлobckий, A. Б (1967), ‘б цehke mepЫ Tpahcцehдehthoctи зчehий E-φyhkiцийMamem. зamemku, 2 (1), 3344.Google Scholar
[4]Sigel, C. L. (1929), ‘Über einige Anwendungen Diophantischer Approximation’Abhand preuss. Acad. Wiss., N I, 170.Google Scholar
[5]Sigel, C. L. (1949), Transcendental numbers (Princeton) University Press.Google Scholar
[6]Шидлobckий, A. Б. (1977), ‘б цehkax Mepбi Tpahcцehдethoctи зhaЧhий E-Φyhkций’ Becmhuk MГy, cepuЯ mamemamuka, mexahuka (6), 310.Google Scholar
[7]Шидлobckий, A. Б. (1959), ‘O kp0Цtepий aлreбpaицeckй heзabЧehий дhoro kлacca цeдbix’, Icy;зБ. AH CCCP, cepuљmamem. 23 (1), 3566.Google Scholar
[8]Шидлobckий, A.Б (1966), ‘K бщeй teopeme; б aлreбpaиЧeckй heзabиmoctизhaЧehий øyhkцийдAh Cccp, 171 (4), 810813.Google Scholar
[9]Шидлobckий, A. Б. (1967), ‘б цehkax mepы tpahcцehдehthoctизhaЧehий E-ций’, Ycnexu mamem. hayk, 22 (3), 245246.Google Scholar
[10]Hecrepehko, Ю (1977), ‘цehkи ΠopЯдkob hyлeй Φh;yhkций дhoro kлacca и иxΠpиπзehий b teopий tpahcцehдehthыx Ч’, N36. AH CCCP, cepu љmamem., 41 (2), 253284.Google Scholar
[11]ШидλobckШ, A. Б. (1959), ‘tpahcцehдehthoctи и aлreиЧeckй heзabиcи зhaЧhий цeλыx øyhkций heotopыx kлaccob’, YCHcy;. зanaucku MГY, ßbin. 186, mame-mamuka, 9, 1170.Google Scholar