@article{FPM_2010_16_5_a3,
author = {K. V\"a\"an\"anen},
title = {Remarks on linear independence of certain $q$-series},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {41--47},
year = {2010},
volume = {16},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a3/}
}
K. Väänänen. Remarks on linear independence of certain $q$-series. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 5, pp. 41-47. http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a3/
[1] Gelfond A. O., “O funktsiyakh, tselochislennykh v tochkakh geometricheskoi progressii”, Mat. sb., 40:1 (1933), 42–47 | Zbl
[2] Gelfond A. O., “O funktsiyakh, prinimayuschikh tselye znacheniya”, Mat. zametki, 1:5 (1967), 509–513 | MR | Zbl
[3] Nesterenko Yu. V., “O mere lineinoi nezavisimosti chisel”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1985, no. 1, 46–49 | MR | Zbl
[4] Amou M., Katsurada M., Väänänen K., “Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré”, Acta Arith., 49:4 (2001), 389–407 | DOI | MR
[5] Amou M., Matala-aho T., Väänänen K., “On Siegel–Shidlovskii's theory for $q$-difference equations”, Acta Arith., 127:4 (2007), 309–335 | DOI | MR | Zbl
[6] Bundschuh P., “Ein Satz über ganze Funktionen und Irrationalitätsaussagen”, Invent. Math., 9 (1970), 175–184 | DOI | MR | Zbl
[7] Bundschuh P., “Arithmetical results on certain $q$-series, I”, Int. J. Number Theory, 4:1 (2008), 25–43 | DOI | MR | Zbl
[8] Matala-aho T., “Remarks on the arithmetic properties of certain hypergeometric series of Gauss and Heine”, Acta Univ. Oulu. Ser. A Sci. Rerum Natur., 219 (1991), 1–112 | MR
[9] Matala-aho T., “On $q$-analogues of divergent and exponential series”, J. Math. Soc. Japan, 61:1 (2009), 291–313 | DOI | MR | Zbl
[10] Väänänen K., “On linear independence of the values of generalized Heine series”, Math. Ann., 325 (2003), 123–136 | DOI | MR | Zbl