# Rational approximations to π and some other numbers

Acta Arithmetica (1993)

- Volume: 63, Issue: 4, page 335-349
- ISSN: 0065-1036

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topMasayoshi Hata. "Rational approximations to π and some other numbers." Acta Arithmetica 63.4 (1993): 335-349. <http://eudml.org/doc/206525>.

@article{MasayoshiHata1993,

author = {Masayoshi Hata},

journal = {Acta Arithmetica},

keywords = {irrationality measure; linear independence measure},

language = {eng},

number = {4},

pages = {335-349},

title = {Rational approximations to π and some other numbers},

url = {http://eudml.org/doc/206525},

volume = {63},

year = {1993},

}

TY - JOUR

AU - Masayoshi Hata

TI - Rational approximations to π and some other numbers

JO - Acta Arithmetica

PY - 1993

VL - 63

IS - 4

SP - 335

EP - 349

LA - eng

KW - irrationality measure; linear independence measure

UR - http://eudml.org/doc/206525

ER -

## References

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- [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. Zbl0536.10028
- [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. Zbl0679.10026
- [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. Zbl0755.11019
- [10] M. Hata, Legendre type polynomials and irrationality measures, J. Reine Angew. Math. 407 (1990), 99-125. Zbl0692.10034
- [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. Zbl0053.36105
- [13] M. Mignotte, Approximations rationnelles de π et quelques autres nombres, Bull. Soc. Math. France Mém. 37 (1974), 121-132. Zbl0286.10017
- [14] G. Rhin, Approximants de Padé et mesures effectives d'irrationalité, in: Progr. in Math. 71, Birkhäuser, 1987, 155-164. Zbl0632.10034
- [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) Zbl0635.10025

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