A note on ( a , b ) -Fibonacci sequences and specially multiplicative arithmetic functions

Emil Daniel Schwab; Gabriela Schwab

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 2, page 237-246
  • ISSN: 0862-7959

Abstract

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A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely ( a , b ) -Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly.

How to cite

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Schwab, Emil Daniel, and Schwab, Gabriela. "A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions." Mathematica Bohemica 149.2 (2024): 237-246. <http://eudml.org/doc/299441>.

@article{Schwab2024,
abstract = {A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a,b)$-Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly.},
author = {Schwab, Emil Daniel, Schwab, Gabriela},
journal = {Mathematica Bohemica},
keywords = {Fibonacci sequence; multiplicative arithmetic function; Binet's formula; Busche-Ramanujan identities; Möbius inversion},
language = {eng},
number = {2},
pages = {237-246},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions},
url = {http://eudml.org/doc/299441},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Schwab, Emil Daniel
AU - Schwab, Gabriela
TI - A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 2
SP - 237
EP - 246
AB - A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a,b)$-Fibonacci sequences and specially multiplicative prime-independent arithmetic functions, are equivalent in the sense that each can be reconstructed from the other. Replacing one with another, the exploration space of both mathematical objects expands significantly.
LA - eng
KW - Fibonacci sequence; multiplicative arithmetic function; Binet's formula; Busche-Ramanujan identities; Möbius inversion
UR - http://eudml.org/doc/299441
ER -

References

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