Rational approximations to π and some other numbers

• Autorzy: Masayoshi Hata
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 63
• Numer: 4
• Strony: 335-349

Daty

wydano

1993

otrzymano

1992-03-03

poprawiono

1992-10-27

Twórcy

autor

Masayoshi Hata

• Institute of Mathematics, Yoshida College, Kyoto University, Kyoto 606, Japan

Bibliografia

• [1] K. Alladi and M. L. Robinson, Legendre polynomials and irrationality, J. Reine Angew. Math. 318 (1980), 137-155.
• [2] F. Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc. 11 (1979), 268-272.
• [3] G. V. Chudnovsky, Hermite-Padé approximations to exponential functions and elementary estimates of the measure of irrationality of π, in: Lecture Notes in Math. 925, Springer, Berlin 1982, 299-322.
• [4] G. V. Chudnovsky, Recurrences, Padé approximations and their applications, in: Lecture Notes in Pure and Appl. Math. 92, Dekker, New York 1984, 215-238.
• [5] D. V. Chudnovsky and G. V. Chudnovsky, Padé and rational approximations to systems of functions and their arithmetic applications, in: Lecture Notes in Math. 1052, Springer, Berlin 1984, 37-84.
• [6] D. V. Chudnovsky and G. V. Chudnovsky, Transcendental methods and theta-functions, in: Proc. Sympos. Pure Math. 49 (2), Amer. Math. Soc., 1989, 167-232.
• [7] J. Dieudonné, Calcul infinitésimal, Hermann, Paris 1968.
• [8] A. K. Dubitskas, Approximation of π/√3 by rational fractions, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1987 (6), 73-76 (in Russian).
• [9] R. Dvornicich and C. Viola, Some remarks on Beukers' integrals, in: Colloq. Math. Soc. János Bolyai 51, Budapest 1987, 637-657.
• [10] M. Hata, Legendre type polynomials and irrationality measures, J. Reine Angew. Math. 407 (1990), 99-125.
• [11] M. Hata, A lower bound for rational approximations to π, J. Number Theory, to appear.
• [12] K. Mahler, On the approximation of π, Nederl. Akad. Wetensch. Proc. Ser. A 56 (1953), 30-42.
• [13] M. Mignotte, Approximations rationnelles de π et quelques autres nombres, Bull. Soc. Math. France Mém. 37 (1974), 121-132.
• [14] G. Rhin, Approximants de Padé et mesures effectives d'irrationalité, in: Progr. in Math. 71, Birkhäuser, 1987, 155-164.
• [15] E. A. Rukhadze, A lower bound for the approximation of ln 2 by rational numbers, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1987 (6), 25-29 (in Russian)