Transcendence of certain series involving binary linear recurrences |
| |
Authors: | Takeshi Kurosawa |
| |
Affiliation: | Nippon Telegraph and Telephone Corporation, NTT Service Integration Laboratories, Midori-Cho 3-9-11, Musashino-Shi, Tokyo 180-8585, Japan |
| |
Abstract: | Duverney and Nishioka [D. Duverney, Ku. Nishioka, An inductive method for proving the transcendence of certain series, Acta Arith. 110 (4) (2003) 305-330] studied the transcendence of , where Ek(z), Fk(z) are polynomials, α is an algebraic number, and r is an integer greater than 1, using an inductive method. We extend their inductive method to the case of several variables. This enables us to prove the transcendence of , where Rn is a binary linear recurrence and {ak} is a sequence of algebraic numbers. |
| |
Keywords: | 11J81 |
本文献已被 ScienceDirect 等数据库收录! |
|