There are infinitely many irrational values of the Riemann zeta function at odd integers;La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 331, Issue 4, 2000, Pages 267-270

  Rivoal, Tanguy ^a  

^a UNIVERSITÉ DE CAEN   (France)

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Indexed keywords

EID: 0034662540     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0764-4442(00)01624-4     Document Type: Article

References (8)

1. [1] Apéry R., Irrationalité de ζ(2) et ζ(3), Astérisque 61 (1979) 11-13.
2. [2] Ball K., Communication personnelle du 17 décembre 1999.
3. [3] Ball K., Communication personnelle du 4 janvier 2000.
4. [4] Beukers F., A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc. 11 (33) (1978) 268-272.
5. [5] Dvornicich R., Viola C., Some remarks on Beukers' integrals, Number Theory, Vol. II, Budapest 1987, Colloq. Math. Soc. János Bolyai, 51, North-Holland, Amsterdam, 1990, pp. 637-657.
6. [6] Nesterenko Y.V., On the linear independence of numbers, Mosc. Univ. Math. Bull. 40 (1) (1985) 69-74. [Traductionde Vest. Mosk. Univ., Ser. I (1) (1985) 46-54.]
7. [6] Nesterenko Y.V., On the linear independence of numbers, Mosc. Univ. Math. Bull. 40 (1) (1985) 69-74. [Traduction de Vest. Mosk. Univ., Ser. I (1) (1985) 46-54.]
8. [7] Nikishin E.M., On the irrationality of the values of the functions F(x,s), Mat. Sbornik 37 (3) (1979) 381-388.