Arithmetical investigations of a certain infinite product

Peter Bundschuh; Keijo Väänänen

Compositio Mathematica (1994)

  • Volume: 91, Issue: 2, page 175-199
  • ISSN: 0010-437X

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Bundschuh, Peter, and Väänänen, Keijo. "Arithmetical investigations of a certain infinite product." Compositio Mathematica 91.2 (1994): 175-199. <http://eudml.org/doc/90288>.

@article{Bundschuh1994,
author = {Bundschuh, Peter, Väänänen, Keijo},
journal = {Compositio Mathematica},
keywords = {infinite products; values of the -analog of the exponential function; arithmetic properties; irrationality measure},
language = {eng},
number = {2},
pages = {175-199},
publisher = {Kluwer Academic Publishers},
title = {Arithmetical investigations of a certain infinite product},
url = {http://eudml.org/doc/90288},
volume = {91},
year = {1994},
}

TY - JOUR
AU - Bundschuh, Peter
AU - Väänänen, Keijo
TI - Arithmetical investigations of a certain infinite product
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 91
IS - 2
SP - 175
EP - 199
LA - eng
KW - infinite products; values of the -analog of the exponential function; arithmetic properties; irrationality measure
UR - http://eudml.org/doc/90288
ER -

References

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  1. 1 Adams, W.W.: Transcendental numbers in the p-adic domain, Amer. J. Math.88 (1966) 279-308. Zbl0144.29301MR197399
  2. 2 André-Jeannin, R.: Irrationalité de la somme des inverses de certaines suites récurrentes, C.R. Acad. Sci. Paris, Ser. I Math.308 (1989) 539-541. Zbl0682.10025MR999451
  3. 3 Bézivin, J.P.: Indépendance linéaire des valeurs des solutions transcendantes de certaines équations fonctionnelles, Manuscripta Math.61 (1988) 103-129. Zbl0644.10025MR939143
  4. 4 Borwein, P.B.: On the irrationality of Σ(1/(qn + r)), J. Number Theory37 (1991) 253-259. Zbl0718.11029
  5. 5 Bundschuh, P., Arithmetische Untersuchungen unendlicher Produkte, Inventiones Math.6 (1969) 275-295. Zbl0195.33703MR238776
  6. 6 Bundschuh, P. und Töpfer, T.: Über lineare Unabhängigkeit (submitted). 
  7. 7 Erdös, P.: On arithmetical properties of Lambert series, J. Indian Math. Soc.(N.S.) 12 (1948) 63-66. Zbl0032.01701MR29405
  8. 8 Exton, H.: q-Hypergeometric Functions and Applications, Ellis Horwood Ltd., Chichester (1983). Zbl0514.33001MR708496
  9. 9 Gel'fond, A.O.: Functions which take on integral values (Russian), Mat. Zametki1 (1967) 509-513; Engl. transl., Math. Notes1, 337-340. Zbl0211.07103MR215795
  10. 10 Lototsky, A.V.: Sur l'irrationalité d'un produit infini, Math. Sbornik12 (54) (1943) 262-272. Zbl0063.03644MR9394
  11. 11 Nesterenko, Yu. V.: On the linear independence of numbers (Russian), Vestnik Moskov. Univ. Ser. I Math Mekh.1 (1985) 46-49; Engl. transl., Moscow Univ. Math. Bull.40, 69-74. Zbl0572.10027MR783238
  12. 12 Popov, A. Yu.: Arithmetical properties of values of some infinite products (Russian). In: Diophantine Approximations 2, Collect. Artic., Moskva (1986) pp. 63-78. Zbl0648.10022MR936655
  13. 13 Popov, A. Yu.: Approximation of values of some infinite products (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh.6 (1990) 3-6; Engl. transl., Moscow Univ. Math. Bull.45, 4-6. Zbl0722.11036MR1095989

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