TY - JOUR
T1 - Irrationality Results for Values of Generalized Tschakaloff Series
AU - Amou, Masaaki
AU - Katsurada, Masanori
N1 - Funding Information:
-The first named author was supported in part by Grant-in-Aid for Scientific Research (09640007), Ministry of Education, Science, Sports and Culture, Japan.
PY - 1999/7
Y1 - 1999/7
N2 - Arithmetical properties of values of the entire functionTq(x)=∑∞n=0x n/q(1/2)n(n+1), whereqis a parameter, q>1, were first studied by L. Tschakaloff (1921,Math. Ann.80, 62-74;84, 100-114). In this paper we introduce a generalization ofTq(x), given by (1.3), and prove the irrationality results for the values of (1.3) at rational points (see Theorem and Corollaries at the end of Section 1). One of the essential tools in the proof is a variant of Mahler's transcendence method, due to J. H. Loxton and A. J. van der Poorten (1977,in"Transcendence Theory: Advances and Applications," pp. 211-226, Academic Press, San Diego).
AB - Arithmetical properties of values of the entire functionTq(x)=∑∞n=0x n/q(1/2)n(n+1), whereqis a parameter, q>1, were first studied by L. Tschakaloff (1921,Math. Ann.80, 62-74;84, 100-114). In this paper we introduce a generalization ofTq(x), given by (1.3), and prove the irrationality results for the values of (1.3) at rational points (see Theorem and Corollaries at the end of Section 1). One of the essential tools in the proof is a variant of Mahler's transcendence method, due to J. H. Loxton and A. J. van der Poorten (1977,in"Transcendence Theory: Advances and Applications," pp. 211-226, Academic Press, San Diego).
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U2 - 10.1006/jnth.1999.2376
DO - 10.1006/jnth.1999.2376
M3 - Article
AN - SCOPUS:0042599174
SN - 0022-314X
VL - 77
SP - 155
EP - 169
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -