TY - JOUR
T1 - Transcendence of certain reciprocal sums of linear recurrences
AU - Duverney, Daniel
AU - Kanoko, Tomoaki
AU - Tanaka, Taka Aki
PY - 2002/10/1
Y1 - 2002/10/1
N2 - Suppose that {Rn}n≥0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers ∑′k ≥ 0 ak/Rcd(k) + b′ where a is a nonzero algebraic number and b, c, and d are integers with c ≥ 1 and d ≥ 2, and that of similarly constructed numbers, using a new theorem on the transcendence of functions.
AB - Suppose that {Rn}n≥0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers ∑′k ≥ 0 ak/Rcd(k) + b′ where a is a nonzero algebraic number and b, c, and d are integers with c ≥ 1 and d ≥ 2, and that of similarly constructed numbers, using a new theorem on the transcendence of functions.
KW - Transcendence, Mahler functions
UR - http://www.scopus.com/inward/record.url?scp=0036776268&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036776268&partnerID=8YFLogxK
U2 - 10.1007/s00605-002-0501-4
DO - 10.1007/s00605-002-0501-4
M3 - Article
AN - SCOPUS:0036776268
SN - 0026-9255
VL - 137
SP - 115
EP - 128
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 2
ER -