Algebraic independence of the numbers ∏ K = 0 ∞ ( 1 - p - 2 K ) with p prime

Kenneth K. Kubota

Séminaire Delange-Pisot-Poitou. Théorie des nombres (1975-1976)

  • Volume: 17, Issue: 1, page 1-9

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Kubota, Kenneth K.. "Algebraic independence of the numbers $\prod ^ \infty _ {K = 0} (1-p^{-2^{K}})$ with $p$ prime." Séminaire Delange-Pisot-Poitou. Théorie des nombres 17.1 (1975-1976): 1-9. <http://eudml.org/doc/110913>.

@article{Kubota1975-1976,
author = {Kubota, Kenneth K.},
journal = {Séminaire Delange-Pisot-Poitou. Théorie des nombres},
language = {eng},
number = {1},
pages = {1-9},
publisher = {Secrétariat mathématique},
title = {Algebraic independence of the numbers $\prod ^ \infty _ \{K = 0\} (1-p^\{-2^\{K\}\})$ with $p$ prime},
url = {http://eudml.org/doc/110913},
volume = {17},
year = {1975-1976},
}

TY - JOUR
AU - Kubota, Kenneth K.
TI - Algebraic independence of the numbers $\prod ^ \infty _ {K = 0} (1-p^{-2^{K}})$ with $p$ prime
JO - Séminaire Delange-Pisot-Poitou. Théorie des nombres
PY - 1975-1976
PB - Secrétariat mathématique
VL - 17
IS - 1
SP - 1
EP - 9
LA - eng
UR - http://eudml.org/doc/110913
ER -

References

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  2. [2] Frobenius ( F.G.). - Über Matrizen aus nicht negativen Elementen, Sitzungsber. preuss. Akad. Wiss., Berlin, 1912, p. 456-477. Zbl43.0204.09JFM43.0204.09
  3. [3] Kubota ( K.K.). - On the algebraic independence of holomorphic solutions of certain functional equations and their values (to appear). Zbl0359.10030MR498423
  4. [4] Kubota ( K.K.). - On a transcendence problem of K. Mahler (to appear). Zbl0335.10038MR498424
  5. [5] Lang ( S.). - Introduction to transcendental numbers. - Reading, Addison-Wesley publishing Company, 1966 (Addison-Wesley Series in Mathematics). Zbl0144.04101MR214547
  6. [6] Lech ( C.). - A note on recurring sequences, Ark. Mat., t. 2, 1953, p. 417- 421. Zbl0051.27801MR56634
  7. [7] Lewis ( D.J.). - Diophantine equations : p-adic methods, "Studies in number theory", p. 25-75. - Englewood Cliffs, Mathematical Association of America, 1969 (Studies in Mathematics, 6). Zbl0218.10035MR241359
  8. [8] Mahler ( K.). - Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Annalen, t. 101, 1929, p. 342-366. Zbl55.0115.01MR1512537JFM55.0115.01
  9. [9] Mahler ( K.). - Über das Verschwinden von Potenzreihen mehrerer Veränderlichen im speziellen Punktfolgen, Math. Annalen, t. 103, 1930, p. 573-587. Zbl56.0185.03MR1512638JFM56.0185.03
  10. [10] Mahler ( K.). - Arithmetische Eigenschaften einer Klasse tranzendental-Tranzendenter Funktionen, Math. Z., t. 32, 1932, p. 545-585. MR1545184JFM56.0186.01
  11. [11] Mahler ( K.). - Remarks on a paper of W. Schwarz, J. Number Theory, t. 1, 1969, p. 512-521. Zbl0184.07602MR249366
  12. [12] Mahler ( K.). - Lectures on transcendental numbers, "1969 Number theory institute", p. 248-274. - Providence, American mathematical Society, 1971 (Proceedings of Symposia in pure Mathematics, 20). Zbl0213.32703MR318071
  13. [13] Turan ( P.). - Eine neue Methode in der Analysis und deren Anwendungen. - Budapest, Akademai Kiado, 1953. Zbl0052.04601MR60548

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