Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of fibonacci numbers

Proceedings of the Japan Academy Series A: Mathematical Sciences

Volumn 73, Issue 7, 1997, Pages 140-142

  Duverney, Daniel ^a   Nishioka, Keiji ^b   Nishioka, Kumiko ^b   Shiokawa, Iekata ^b  

^a Keio University ^*  (France)

^b KEIO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944436347     PISSN: 03862194     EISSN: None     Source Type: Journal    
DOI: 10.3792/pjaa.73.140     Document Type: Article

References (11)

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3. D. Duverney, Ke. Nishioka, Ku. Nishioka, and I. Shiokawa: Transcendence of Jacobi's theta series. Proc. Japan Acad., 72A, 202-203 (1996).
4. D. Duverney, Ke. Nishioka, Ku. Nishioka, and I. Shiokawa: Transcendence of Jacobi's theta series and related results. Number Theory-Diophantine, Computational and Algebraic Aspects, Proc. Cont. Number Theory Eger 1996 (eds. K. Györy, A. Pethö, and V. T. Sos). W. de Gruyter (to appear).
5. T. Matala-Aho: On Diophantine approximations of the Rogers-Ramanujan continued fraction. J. Number Theory, 45 (2), 215-227 (1983).
6. Yu. V. Nesterenko: Modular functions and transcendence problems. C. R. Acad. Sci. Paris, ser. 1, 322, 909-914 (1996).
7. Yu. V. Nesterenko: Modular functions and transcendence problems. Math. Sb., 187 (9), 65-96 (1996) (Russiam);
8. English transl. Sbornik Math. 187 (9-10), 1319-1348 (1996).
9. C. F. Osgood: The diophantine approximation of certain continued fractions. Proc. Amer. Math. Soc., 3, 1-7 (1977).
10. I. Shiokawa: Rational approximation to the Rogers-Ramanujan continued fractions. Acta Arith., L, 23-30 (1988).
11. I. J. Zucker: The summation of series of hyperbolic functions. SIAM J. Math. Anal., 10, 192-206 (1979).