Recurrent Sequences and Affine Functional Equations

✍ Scribed by Lutz Lucht; Cordelia Methfessel

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 388 KB
• Volume: 57
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1996.0036

✦ Synopsis

Sa rko zy and other authors have characterized the multiplicative and the additive sequences among the solutions g: N Ä C of homogeneous linear recurrence equations with complex coefficients. Their results are special cases of a much more general theorem concerning recurrent sequences g satisfying certain functional equations of the type g(nq+a)=q*g(n)+a* (n=1, ..., N) for sufficiently large q, N # N with some coefficients a # N, a*, q* # C, q*{0. The results and methods of proof given in the present paper are new.

1996 Academic Press, Inc.

Sa rko zy [7], Lova sz et al. [2], Heppner and Maxsein [1] and Maxsein

[3] have studied recurrent and ultimately recurrent sequences g which, in addition, are multiplicative (i.e., g(1)=1 and g(mn)= g(m) g(n) for all coprime m, n # N) or additive (i.e., g(mn)= g(m)+ g(n) for all coprime article no. 0036