On the measure of approximation of the number π by algebraic numbers

Mathematical Notes

Volumn 66, Issue 4, 1999, Pages 395-403

  Aleksentsev, Yu M ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Approximations of , Laurent interpolation determinant; Logarithm of an algebraic number; Measure of transcendence

Indexed keywords

EID: 27544448024     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02679086     Document Type: Article

References (7)

1. N. I. Fel'dman, "The approximation of certain transcendental numbers. I," Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 15, No. 1, 53-74 (1951).
2. N. I. Fel'dman, "The measure of transcendence of the number π," Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 24, No. 3, 357-368 (1960).
3. N. I. Fel'dman, "A constant in the estimation of the measure of transcendence of the number π," in: Diophantine Approximations [in Russian], Pt. 1, Izd. Moskov. Univ., Moscow (1985).
4. M. Val'dshmidt [M. Waldschmidt] and Yu. M. Nesterenko, "On the approximation of the values of the exponential function and of the logarithm by algebraic numbers," in: Diophantine Approximations. A Collection of Papers Dedicated to the Memory of Professor N. I. Fel'dman [in Russian], Vol. 2, Mathematical Transactions, Center for Applied Research at the Faculty of Mechanics and Mathematics of Moscow State University, Moscow (1996), pp. 23-42.
5. Kunrui Yu, "Linear forms in p-adic logarithms," Pt. I, Acta Arith., 53, 105-113 (1989);
6. Pt II, Compositio Math., 74, 15-113 (1990).
7. N. I. Fel'dman, Hilbert's Seventh Problem [in Russian], Izd. Moskov. Univ., Moscow (1982).