The relationship between Fibonacci number and Riemann zeta-function in the sense of Ramanujan constant

Abstract Riemann zeta-function has had a lot of research progress and applications in recent 50 years. The Fibonacci number is also widely used. This paper gives a derivation of the relation between the Riemann zeta function and the Fibonacci number. Generating functions are used to process the Fibonacci number, and then associate the Fibonacci number with the Bernoulli number. The connection of functions makes the appearance of Zeta possible, and finally, the relation between the Fibonacci number and the Zeta function is obtained.